NIMCET Vector Previous Year Question Paper and Solution with PDF

Solution

Qus : 2NIMCET PYQ

If $\vec{a}, \vec{b}$ are unit vectors such that $2\vec{a}+\vec{b} =3$ then which of the following statement is true?

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Solution

Qus : 3NIMCET PYQ

$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ is the angle between $\vec{a}=\hat{i}-2x\hat{j}+2y\hat{k}$ & $\vec{b}=x\hat{i}+\hat{j}+y\hat{k}$ then possible values of (x,y) that lie on the locus

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Solution

Qus : 4NIMCET PYQ

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes,then the sum of the magnitude of the projections on each of the axis is

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Solution

Qus : 5NIMCET PYQ

The value of non-zero scalars α and β such that for all vectors

and

such that

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Solution

Qus : 6NIMCET PYQ

A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnitude of its moment about the line joining the origin to the point (12,3,4) is

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Solution

Qus : 7NIMCET PYQ

The position vectors of the vertices

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Solution

Qus : 8NIMCET PYQ

Not Available right now

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Solution

Qus : 9NIMCET PYQ

Let $\vec{a}, \vec{b}, \vec{c} $ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then c is

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Solution

$\vec{a}=a\hat{i}+a\hat{j}+c\hat{k}\, ,\, \vec{b}=\hat{i}+\hat{k}\, \&\, \vec{c}=c\hat{i}+c\hat{j}+b\hat{k}$ are coplanar.

$\Rightarrow\begin{vmatrix}{a} & {a} & {c} \\ {1} & {0} & {1} \\ {c} & {c} & {b}\end{vmatrix}=0$

$\Rightarrow-ac-ab+ac+{c}^2=0$

$\Rightarrow{c}^2=ab$

Qus : 10NIMCET PYQ

The value of m for which volume of the parallelepiped is 4 cubic units whose three edges are represented by a = mi + j + k, b = i – j + k, c = i + 2j –k is

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Solution

Qus : 11NIMCET PYQ

The number of distinct real values of $\lambda$ for which the vectors ${\lambda}^2\hat{i}+\hat{j}+\hat{k},\, \hat{i}+{\lambda}^2\hat{j}+j$ and $\hat{i}+\hat{j}+{\lambda}^2\hat{k}$ are coplanar is

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Solution

Qus : 12NIMCET PYQ

If the volume of the parallelepiped whose adjacent edges are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\alpha \hat{j}+2\hat{k}$ and $\vec{c}=\hat{i}+2\hat{j}+\alpha \hat{k}$ is 15, then $\alpha$ is equal to

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Solution

Qus : 13NIMCET PYQ

Let $\vec{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}$ be another vector such that $\vec{a}.\vec{b}=14$ and $\vec{a} \times \vec{b}=3\hat{i}+\hat{j}-8\hat{k}$ the vector $\vec{b}$ =

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Solution

Qus : 14NIMCET PYQ

If $\vec{a}=\lambda \hat{i}+\hat{j}-2\hat{k}$ , $\vec{b}=\hat{i}+\lambda \hat{j}-2\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}+\hat{k}$ and $\begin{bmatrix}{\vec{a}} & {\vec{b}} & {\vec{c}} \end{bmatrix}=7$, then the values of the $\lambda$ are

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Solution

Qus : 15NIMCET PYQ

If $(\vec{a} \times \vec{b}) \times \vec{c}= \vec{a} \times (\vec{b} \times \vec{c})$, then

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Solution

Qus : 16NIMCET PYQ

Let $\vec{a}=2\widehat{i}\, +\widehat{j}\, +2\widehat{k}$ , $\vec{b}=\widehat{i}-\widehat{j}+2\widehat{k}$ and $\vec{c}=\widehat{i}+\widehat{j}-2\widehat{k}$ are are three vectors. Then, a vector in the plane of $\vec{a}$ and $\vec{c}$ whose projection on $\vec{b}$ is of magnitude $\frac{1}{\sqrt{6}}$ is

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Solution

Qus : 17NIMCET PYQ

If the position vector of A and B relative to O be $\widehat{i}\, -4\widehat{j}+3\widehat{k}$ and $-\widehat{i}\, +2\widehat{j}-\widehat{k}$ respectively, then the median through O of ΔABC is:

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Solution

Qus : 18NIMCET PYQ

The area of the triangle formed by the vertices whose position vectors are $3\widehat{i}+\widehat{j}$ , $5\widehat{i}+2\widehat{j}+\widehat{k}$ , $\widehat{i}-2\widehat{j}+3\widehat{k}$ is

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Solution

Qus : 19NIMCET PYQ

If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}$ , $(a,b,c\ne1)$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

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Solution

Qus : 20NIMCET PYQ

The direction cosines of the vector a = (- 2i + j – 5k) are

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Solution

Qus : 21NIMCET PYQ

Let $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=2\hat{i}-\hat{k}$, the point of intersection of the lines $\vec{r}\times\vec{a}=\vec{b}\times\vec{a}$ and $\vec{r}\times\vec{b}=\vec{a}\times\vec{b}$ is

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Solution

Qus : 22NIMCET PYQ

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are vectors such that $\vec{a}$+$\vec{b}$+$\vec{c}$ = 0 and |$\vec{a}$| =7, $\vec{b}$=5, |$\vec{c}$| = 3, then the angle between the vectors $\vec{b}$ and $\vec{c}$

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Solution

Qus : 23NIMCET PYQ

and

, (a ≠ b ≠ c ≠ 1) are co-planar, then the value of

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Solution

Qus : 24NIMCET PYQ

Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a x (a x c) - b = 0, then the acute angle between a and c is

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Solution

Qus : 25NIMCET PYQ

Let

and

be three vector such that |

| = 2, |

| = 3, |

| = 5 and

= 0. The value of

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Solution

Qus : 26NIMCET PYQ

and

are unit vectors, then

does not exceeds

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Solution

Qus : 27NIMCET PYQ

= (i + 2j - 3k) and

=(3i -j + 2k), then the angle between (

) and (

)

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Solution

Qus : 28NIMCET PYQ

The vector

lies in the plane of the vector

and

and bisects the angle between

and

. Then which of the following gives possible values of

and

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Solution

Qus : 29NIMCET PYQ

A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?

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Solution

Qus : 30NIMCET PYQ

Angle between $\vec{a}$ and $\vec{b}$ is $120{^{\circ}}$. If $|\vec{b}|=2|\vec{a}|$ and the vectors , $\vec{a}+x\vec{b}$ , $\vec{a}-\vec{b}$ are at right angle, then $x=$

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Solution

Qus : 31NIMCET PYQ

If $\vec{e_1}=(1,1,1)$ and $\vec{e_2}=(1,1,-1)$ and $\vec{a}$ and $\vec{b}$ and two vectors such that $\vec{e_2}=\vec{a}+2\vec{b}$ , then angle between $\vec{a}$ and $\vec{b}$

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Solution

Qus : 32NIMCET PYQ

A cube is made up of 125 one cm. square cubes placed on a table. How many squares are visible only on three sides?

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Solution

Qus : 33NIMCET PYQ

are three non-coplanar vectors, then

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Solution

Qus : 34NIMCET PYQ

Two forces F₁ and F₂ are used to pull a car, which met an accident. The angle between the two forces is θ . Find the values of θ for which the resultant force is equal to

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Solution

Qus : 35NIMCET PYQ

are four vectors such that

is collinear with

and

is collinear with

then

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Solution

Qus : 36NIMCET PYQ

Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the point (2, −1, −3) to (5, −1, 1). The total work done by the force is

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Solution

Qus : 37NIMCET PYQ

The position vectors of points A and B are

and

. Then the position vector of point p dividing AB in the ratio m : n is

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Solution

Qus : 38NIMCET PYQ

If a, b, c are three non-zero vectors with no two of which are collinear, a + 2b is collinear with c and b + 3c is collinear with a , then | a + 2b + 6c | will be equal to

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Solution

Qus : 39NIMCET PYQ

Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is

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Solution

Qus : 40NIMCET PYQ

If the volume of a parallelepiped whose adjacent edges are

a = 2i + 3j + 4k,

b = i + αj + 2k

c = i + 2k + αk

is 15, then α =

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Solution

Qus : 41NIMCET PYQ

If $\overrightarrow{{a}}$ and $\overrightarrow{{b}}$ are vectors in space, given by $\overrightarrow{{a}}=\frac{\hat{i}-2\hat{j}}{\sqrt[]{5}}$ and $\overrightarrow{{b}}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt[]{14}}$, then the value of$(2\vec{a} + \vec{b}).[(\vec{a} × \vec{b}) × (\vec{a} – 2\vec{b})]$ is

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Solution

Qus : 42NIMCET PYQ

Let $\vec{A} = 2\hat{i} + \hat{j} – 2\hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$, If $\vec{C}$ is a vector such that $|\vec{C} – \vec{A}| = 3$ and the angle between A × B and C is ${30^{\circ}}$, then $|(\vec{A} × \vec{B}) × \vec{C}|$ = 3 then the value of $\vec{A}.\vec{C}$ is equal to

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