If, a, = 2, b, = 3 and, 2a - b, = 5, then, 2a + b, equals to Option 1: 15 Option 2: 7 Option 3: 5 Option 4: 1

Answer: 5. Solution: 2a-b, ^2 = 4, a, ^2+, b, ^2-4ab = 16+9-4ab = 25, so a*b=0. Then, 2a+b, ^2 = 16+9+0 = 25, giving, 2a+b, = 5.

Algebra

Vector Algebra

Easy

core

If $|\vec{a}| = 2$ , $|\vec{b}| = 3$ and $|2\vec{a} - \vec{b}| = 5$ , then $|2\vec{a} + \vec{b}|$ equals to

✅ Correct Option: 3

$|2\vec{a}-\vec{b}|^2 = 4|\vec{a}|^2+|\vec{b}|^2-4\vec{a}\cdot\vec{b} = 16+9-4\vec{a}\cdot\vec{b} = 25$ , so $\vec{a}\cdot\vec{b}=0$ .

Then $|2\vec{a}+\vec{b}|^2 = 16+9+0 = 25$ , giving $|2\vec{a}+\vec{b}| = 5$ .

2025: 14 May Shift 1

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$ , then the angle between $\vec{a}$ and $\vec{b}$ is

2022: 10 Aug Shift 1

If $|\vec{a}| = 8$ , $|\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 12$ , then the value of $\vec{a} \cdot \vec{b}$ is

2022: 10 Aug Shift 1

If $|\vec{a}| = 3|\vec{b}|$ , $|\vec{b}| = 2$ and angle between $\vec{a}$ and $\vec{b}$ is $60^\circ$ , then $|\vec{a} - \vec{b}|$ is equal to:

2023: 30 May Shift 3

In $\triangle ABC$ :

(A) $\vec{AB} + \vec{BC} + \vec{CA} = \vec{O}$

(B) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{O}$

(D) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{O}$

(E) $\vec{AB} - \vec{CB} - \vec{CA} = \vec{O}$

Choose the correct answer from the options given below :

2025: 30 May Shift 2

A unit vector perpendicular to the vectors $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ is

2022: 23 Aug Shift 1

If $-3 \leq k \leq 1$ and $|\vec{a}| = 2$ then $|k\vec{a}|$ is