If a, b, c are three vectors such that, a, = 2, b, = 5, c, = 3 and a + 2b - 3c = 0, then angle between b and c is equal to: Option 1: ^(-1)((-23)/40) Option 2: ^(-1)(-177/180) Option 3: ^(-1)(23/40) Option 4: ^(-1)(177/180)

Answer: ^(-1)(177/180). Solution: From the relation, a = 3 c - 2 b, so, a, ^2 = 9, c, ^2 + 4, b, ^2 - 12( b* c). Thus 4 = 81 + 100 - 12( b* c), giving b* c = 177/12. So = (177/12)/15 = 177/180.

Algebra

Vector Algebra

Medium

core

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 2, |\vec{b}| = 5, |\vec{c}| = 3$ and $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$ , then angle between $\vec{b}$ and $\vec{c}$ is equal to:

$\cos^{-1}\left(\dfrac{-23}{40}\right)$

$\cos^{-1}\left(-\dfrac{177}{180}\right)$

$\cos^{-1}\left(\dfrac{23}{40}\right)$

$\cos^{-1}\left(\dfrac{177}{180}\right)$

✅ Correct Option: 4

Thus $4 = 81 + 100 - 12(\vec b\cdot\vec c)$ , giving $\vec b\cdot\vec c = 177/12$ .

So $\cos\theta = (177/12)/15 = 177/180$ .

2025: 15 May Shift 1

The position vector of a point which divides the line joining the points with position vectors $(\vec{a} - 2\vec{b})$ and $(2\vec{a} + \vec{b})$ externally in the ratio 2:1, is

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Angle between $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$	(I) $\pi$
(B) Angle between $\hat{i} - \hat{j} + \hat{k}$ and $-\hat{i} + \hat{j} - \hat{k}$	(II) $\frac{3\pi}{4}$
(C) Angle between $\hat{i} + \hat{j}$ and $-\hat{i}$	(III) $\frac{\pi}{4}$
(D) Angle between $\hat{i} + \hat{k}$ and $\hat{k}$	(IV) $\frac{\pi}{2}$

Choose the correct answer from the options given below:

2025: 29 May Shift 2

If $\vec{a}$ and $\vec{b}$ are two non-zero orthogonal vectors, then $|\vec{a} + \vec{b}|$ is equal to

2025: 3 June Shift 2

Let $\theta$ be the angle between two vectors $\vec{a}$ and $\vec{b}$ . Then match List-I with List-II

List-I	List-II
(A) $\sin \theta$	(I) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert \vert \vec{b}\vert }$
(B) $\cos \theta$	(II) $\vert \vec{a} \times \vec{b}\vert$
(C) Area of the parallelogram with adjacent sides represented by $\vec{a}$ and $\vec{b}$	(III) $\dfrac{\vec{a} \cdot \vec{b}}{\vert \vec{a}\vert }$
(D) Projection of $\vec{a}$ on $\vec{b}$	(IV) $\dfrac{\vert \vec{a} \times \vec{b}\vert }{\vert \vec{a}\vert \vert \vec{b}\vert }$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

There are two unit vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}+\vec{b}|=\sqrt{3}$ and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vert \vec{a} - \vec{b} \vert$	I.	$0$
B.	$\cos\theta$	II.	$1$
C.	$\theta$	III.	$\dfrac{1}{2}$
D.	$\sin 3\theta$	IV.	$\dfrac{\pi}{3}$

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

In a triangle, $\triangle ABC$ , the sides AB and AC are represented by vectors $\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} - \hat{k}$ respectively. The length of median drawn from vertex A to BC is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)