Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Vector Algebra

Multiple Choice Questions

521.

If vectors $\hat{i} + \hat{j} + \hat{k}, \hat{i} - \hat{j} + \hat{k} and 2 \hat{i} + 3 \hat{j} + λ \hat{k}$ are coplanar, then $λ$ is equal to

522.

Given, $\vec{a} ⊥ \vec{b}$ , $|\vec{a}| = 1$ and if $(\vec{a} + 3 \vec{b}) (2 \vec{a} - \vec{b}) = - 10$ , $|\vec{b}|$ is equal to

523.

$[\vec{a} + \vec{b} \vec{b} + \vec{c} \vec{c} + \vec{a}] = [\vec{a} \vec{b} \vec{c}]$ , then

$[\vec{a} \vec{b} \vec{c}] = 1$
$\vec{a} \vec{b} \vec{c}$ are coplanar
$[\vec{a} \vec{b} \vec{c}] = - 1$
$\vec{a} \vec{b} \vec{c}$ are mutually perpendicular

524.

Area of rhombus is ..., where diagonals are $\vec{a} = 2 \hat{i} - 3 \hat{j} + 5 \hat{k} and \vec{b} = - \hat{i} + \hat{j} + \hat{k}$

$\sqrt{21.5}$
$\sqrt{31.5}$
$\sqrt{28.5}$
$\sqrt{38.5}$

525.

$\frac{\vec{a} . (\vec{b} \times \vec{c})}{\vec{b} . (\vec{c} \times \vec{a})} + \frac{\vec{b} . (\vec{a} \times \vec{b})}{\vec{a} . (\vec{b} \times \vec{c})}$ is equal to

1
2
0
$\infty$

526.

If $|\vec{a}| = |\vec{b}| = 1 and |\vec{a} + \vec{b}| = \sqrt{3}$ , then the value of $(3 \vec{a} - 4 \vec{b}) . (2 \vec{a} + 5 \vec{b})$ is

- 21
$- \frac{21}{2}$
21
$\frac{21}{2}$

527.

If $\vec{a}$ is perpendicular to $\vec{b} and \vec{c}$ , $|\vec{a}|$ = 2, $|\vec{b}|$ = 3, $|\vec{c}|$ = 4 and the angle between $\vec{b} and \vec{c}$ is $\frac{2 π}{3}$ , then [ $\vec{a} \vec{b} \vec{c}$ ] is equal to

$4 \sqrt{3}$
$6 \sqrt{3}$
$12 \sqrt{3}$
$18 \sqrt{3}$

528.

If $\vec{a}$ , $\vec{b} and \vec{c}$ are perpendicular to $\vec{b} + \vec{c}$ , $\vec{c} + \vec{a}$ and $\vec{a} + \vec{b}$ respectively and if $|\vec{a} + \vec{b}|$ = 6, $|\vec{b} + \vec{c}|$ = 8 and $|\vec{c} + \vec{a}|$ = 10 then $|\vec{a} + \vec{b} + \vec{c}|$ is equal to

$5 \sqrt{2}$
50
$10 \sqrt{2}$
10

529.

If the vectors $\vec{a} + λ \vec{b} + 3 \vec{c}$ , $- 2 \vec{a} + 3 \vec{b} - 4 \vec{c}$ and $\vec{a} - 3 \vec{b} + 5 \vec{c}$ are coplanar, then the value of $λ$ is

530.
If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ , $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$ , then anle between $\vec{a} and \vec{b}$ is

$\frac{π}{6}$

$\frac{2 π}{3}$

$\frac{5 π}{3}$

$\frac{π}{3}$

$\frac{π}{3}$

$\vec{a} + \vec{b} + \vec{c} = \vec{0}, |\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7 ∴ \vec{c} = - (\vec{a} + \vec{b}) \Rightarrow {|\vec{c}|}^{2} = \vec{c} . \vec{c} = (\vec{a} + \vec{b}) . (\vec{a} + \vec{b}) \Rightarrow {|\vec{c}|}^{2} = {|\vec{a}|}^{2} + {|\vec{b}|}^{2} + 2 |\vec{a}| |\vec{b}| \Rightarrow {|\vec{c}|}^{2} = {|\vec{a}|}^{2} + {|\vec{b}|}^{2} + 2 |\vec{a}| |\vec{b}| \cos (θ) \Rightarrow 49 = 9 + 25 + 2 \times 3 \times 5 \cos (θ) \Rightarrow 15 = 30 \cos (θ) \Rightarrow \cos (θ) = \frac{1}{2} \Rightarrow θ = \frac{π}{3}$

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

530. If a→ + b→ + c→ = 0→, a→ = 3, b→ = 5, c→ = 7, then anle between a→ and b→ is π6 2π3 5π3 π3

530.
If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ , $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$ , then anle between $\vec{a} and \vec{b}$ is

$\frac{π}{6}$

$\frac{2 π}{3}$

$\frac{5 π}{3}$

$\frac{π}{3}$