NIMCET Vector Previous Year Questions (PYQs) – Page 10 of 10
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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
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
and .
Then the position vector of point p dividing AB in
the ratio m : n is1
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Solution
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
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
If $\vec{a}, \vec{b}$ are vector such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and
$\vec{a}\times (2\hat{i}+3\hat{j}+4\hat{k}) = (2\hat{i}+3\hat{j}+4\hat{k})\times \vec{b}$, then a possible value of $(\vec{a}+\vec{b})\cdot(-7\hat{i}+2\hat{j}+3\hat{k})$ is
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Solution
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
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
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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Solution
If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}|=13$, $|\vec{b}|=5$ and $\vec{a} . \vec{b} =60$then the value of $|\vec{a} \times \vec{b}|$ is
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Solution
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