If a and b are two non-zero vectors such that, 2a+b, =, b, and a+b 0, then the angle between a+b and a, is Option 1: 30° Option 2: 60° Option 3: 90° Option 4: 0°

Answer: 90°. Solution: Squaring the given condition: 4, a, ^2 + 4ab +, b, ^2 =, b, ^2, so ab = -, a, ^2. Then (a+b)a =, a, ^2 + ab = 0. Since neither vector is zero, the angle is 90^.

Algebra

Vector Algebra

Medium

core

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|2\vec{a}+\vec{b}|=|\vec{b}|$ and $\vec{a}+\vec{b}\ne \vec{0}$ , then the angle between $\vec{a}+\vec{b}$ and $\vec{a}$ , is

30°

60°

90°

0°

✅ Correct Option: 3

Squaring the given condition: $4|\vec{a}|^2 + 4\vec{a}\cdot\vec{b} + |\vec{b}|^2 = |\vec{b}|^2$ , so $\vec{a}\cdot\vec{b} = -|\vec{a}|^2$ .

Then $(\vec{a}+\vec{b})\cdot\vec{a} = |\vec{a}|^2 + \vec{a}\cdot\vec{b} = 0$ .

Since neither vector is zero, the angle is $90^\circ$ .

2025: 26 May Shift 2

If $\vec{a}$ , $\vec{b}$ and $\sqrt{3}\vec{a} + \vec{b}$ are unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ is:

2025: 16 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Angle between î and -ĵ is	(I) $\frac{\pi}{6}$
(B) Angle between 2î + k̂ and 10î + 5k̂ is	(II) $\frac{\pi}{4}$
(C) Angle between î and î + ĵ is	(III) 2π
(D) Angle between √3ĵ - k̂ and ĵ is	(IV) $\frac{\pi}{2}$

Choose the correct answer from the options given below:

2026: 22 May Shift 1

If $|\vec a|=2, |\vec b|=7$ and $\vec a\times\vec b=3\hat i+2\hat j+6\hat k$ , then angle between $\vec a$ and $\vec b$ 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: 15 May Shift 2

If $\hat{a}, \hat{b}$ and $\hat{c}$ are three unit vectors and $\hat{a} + \hat{b} + \hat{c} = \vec{0}$ , then the angle between $\hat{a}$ and $(-\hat{b})$ is

2025: 14 May Shift 2

If $\vec{a}$ is a unit vector perpendicular to both the vectors $\vec{b} = \hat{j} + \hat{2k}$ and $\vec{c} = \hat{i} + 2\hat{j}$ , then $\hat{a}$ is equal to

If a⃗\vec{a}a and b⃗\vec{b}b are two non-zero vectors such that ∣2a⃗+b⃗∣=∣b⃗∣|2\vec{a}+\vec{b}|=|\vec{b}|∣2a+b∣=∣b∣ and a⃗+b⃗≠0⃗\vec{a}+\vec{b}\ne \vec{0}a+b=0, then the angle between a⃗+b⃗\vec{a}+\vec{b}a+b and a⃗\vec{a}a, is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|2\vec{a}+\vec{b}|=|\vec{b}|$ and $\vec{a}+\vec{b}\ne \vec{0}$ , then the angle between $\vec{a}+\vec{b}$ and $\vec{a}$ , is