If a unit vector a makes an angle /3 with i, /4 with j and an acute angle with k, then the respective value of and a are Option 1: /3 and 3/2 i+ j/2+3/2 k Option 2: /6 and 3/2 i+ j/2+3/2 k Option 3: /3 and i/2+ j/2+ k/2 Option 4: /6 and i/2+ j/2+ k/2

The answer is '/3 and i/2+ j/2+ k/2'. View full solution:

CUET Mathematics - If a unit vector a makes an angle /3 with i, /4 with j and an acute angle with k, then the respective value of and a are | PYQs + Solutions

CUET Mathematics 2026 29th May Shift 1

Algebra

Medium

core

$\dfrac{\pi}{3}$ and $\dfrac{\sqrt3}{2}\hat i+\dfrac{\hat j}{\sqrt2}+\dfrac{\sqrt3}{2}\hat k$

$\dfrac{\pi}{6}$ and $\dfrac{\sqrt3}{2}\hat i+\dfrac{\hat j}{\sqrt2}+\dfrac{\sqrt3}{2}\hat k$

$\dfrac{\pi}{3}$ and $\dfrac{\hat i}{2}+\dfrac{\hat j}{\sqrt2}+\dfrac{\hat k}{2}$

$\dfrac{\pi}{6}$ and $\dfrac{\hat i}{2}+\dfrac{\hat j}{\sqrt2}+\dfrac{\hat k}{2}$

✅ Correct Option: 3

Related questions:

22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	Area of triangle $\Delta$ with adjacent sides $\vec{a}$ and $\vec{b}$	(I)	$\vec{a} \times \vec{b}$
(B)	Area of parallelogram with adjacent sides $\vec{a}$ and $\vec{b}$	(II)	$\frac{1}{2}\lvert \vec{a} \times \vec{b} \rvert$
(C)	$(\vec{a} - \vec{b}) \times (\vec{a} + \vec{b})$	(III)	$\lvert \vec{a} \times \vec{b} \rvert$
(D)	$\lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin\theta \hat{n}$ , where symbols have their usual meaning	(IV)	$2(\vec{a} \times \vec{b})$

Choose the correct answer from the options given below :

15 May Shift 2

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors such that $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$ , then the value of $2\vec{a}.\vec{b} - 6\vec{b}.\vec{c} - 3\vec{c}.\vec{a}$ is

30th May Shift 2

If $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$ , then which of the following statements are correct?

(A) $\vec{a}$ and $\vec{b}$ are perpendicular to each other.

(B) $\vec{a}$ and $\vec{b}$ are parallel.

(D) Projection of $\vec{a}$ on $\vec{b}$ = 0.

Choose the correct answer from the options given below:

CUET Mathematics 2026 29th May Shift 1 PYQs

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