If \veca, \vecb are unit vectors such that 2\veca+\vecb =3 then which of the ...

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Question Id : 11521 | Context :NIMCET 2023

$\vec{a}, \vec{b}$ are unit vectors such that

$2\vec{a}+\vec{b} =3$ then which of the following statement is true?

🎥 Video solution / Text Solution of this question is given below:

Given: $\vec{a}, \vec{b}$ are unit vectors and

$2\vec{a} + \vec{b} = 3$

Take magnitude on both sides:

$|2\vec{a} + \vec{b}| = 3 \Rightarrow |2\vec{a} + \vec{b}|^2 = 9$

Use identity:

$|2\vec{a} + \vec{b}|^2 = 4|\vec{a}|^2 + |\vec{b}|^2 + 4(\vec{a} \cdot \vec{b}) = 4 + 1 + 4(\vec{a} \cdot \vec{b}) = 5 + 4(\vec{a} \cdot \vec{b})$

Set equal to 9:

$5 + 4(\vec{a} \cdot \vec{b}) = 9 \Rightarrow \vec{a} \cdot \vec{b} = 1 \Rightarrow \cos\theta = 1 \Rightarrow \theta = 0^\circ$

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