M.C.Q (1 Marks)

MCQ 11 Mark

If $\theta$ is the angle between the vectors $2\hat{\text{i}}-2\hat{\text{j}}+4\hat{\text{k}}$ and $3\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}},$ then $\sin\theta=$

A
$\frac{2}{3}$
B
$\frac{2}{\sqrt{7}}$
✓
$\frac{\sqrt{2}}{7}$
D
$\sqrt{\frac{2}{7}}$

Answer

Correct option: C.

$\frac{\sqrt{2}}{7}$

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MCQ 21 Mark

A unit vector perpendicular to both $\hat{\text{i}}+\hat{\text{j}}$ and $\hat{\text{j}}+\hat{\text{k}}$ is:

A
$\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$
B
$\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$
C
$\frac{1}{\sqrt{3}}\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)$
✓
$\frac{1}{\sqrt{3}}\big(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)$

Answer

Correct option: D.

$\frac{1}{\sqrt{3}}\big(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)$

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MCQ 31 Mark

vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are inclined at angle $\theta=120^\circ.$ if $|\vec{\text{a}}|=1,\big|\vec{\text{b}}\big|=2,$ then $\big[\big(\vec{\text{a}}+3\vec{\text{b}}\big)\times\big(3\vec{\text{a}}-\vec{\text{b}}\big)\big]^2$ is equal to:

✓
$300$
B
$325$
C
$275$
D
$225$

Answer

Correct option: A.

$300$

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MCQ 41 Mark

If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=4,\big|\vec{\text{a}}.\vec{\text{b}}\big|=2,$ then $|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2=$

A
$6$
B
$2$
✓
$20$
D
$8$

Answer

Correct option: C.

$20$

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MCQ 51 Mark

The value of $\hat{\text{i}}.\big(\hat{\text{j}}\times\hat{\text{k}}\big)+\hat{\text{j}}.\big(\hat{\text{i}}\times\hat{\text{k}}\big)+\hat{\text{k}}.\big(\hat{\text{i}}\times\hat{\text{j}}\big),$ is:

A
$0$
B
$-1$
✓
$1$
D
$3$

Answer

Correct option: C.

$1$

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MCQ 61 Mark

If $\vec{\text{a}}$ is any vector, then $\big(\vec{\text{a}}\times\hat{\text{i}}\big)^2+\big(\vec{\text{a}}\times\hat{\text{j}}\big)^2+\big(\vec{\text{a}}\times\hat{\text{k}}\big)^2=$

A
$\vec{\text{a}}^2$
✓
$2\vec{\text{a}}^2$
C
$3\vec{\text{a}}^2$
D
$4\vec{\text{a}}^2$

Answer

Correct option: B.

$2\vec{\text{a}}^2$

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MCQ 71 Mark

If $\theta$ is the angle between any two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\big|\vec{\text{a}}.\vec{\text{b}}\big|=\big|\vec{\text{a}}\times\vec{\text{b}}\big|$ when $\theta$ is equal to:

A
$0$
✓
$\frac{\pi}{4}$
C
$\frac{\pi}{2}$
D
$\pi$

Answer

Correct option: B.

$\frac{\pi}{4}$

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MCQ 81 Mark

If $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},\vec{\text{b}}=-\hat{\text{i}}+2\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{c}}=-\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}},$ then a unit vector normal to the vectors $\vec{\text{a}}+\vec{\text{b}}$ and $\vec{\text{b}}-\vec{\text{c}}$ is:

✓
$\hat{\text{i}}$
B
$\hat{\text{j}}$
C
$\hat{\text{k}}$
D
$\text{None of these}$

Answer

Correct option: A.

$\hat{\text{i}}$

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MCQ 91 Mark

The vector $\vec{\text{b}}=3\hat{\text{i}}+4\hat{\text{k}}$ is to be written as the sum of a vector $\vec{\alpha}$ parallel to $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}$ and a vector $\vec{\beta}$ perpendicular to $\vec{\text{a}}.$ Then $\vec{\alpha}=$

A
$\frac{3}{2}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
✓
$\frac{2}{3}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
C
$\frac{1}{2}\big(\hat{\text{i}}+\hat{\text{j}}\big)$
D
$\frac{1}{3}\big(\hat{\text{i}}+\hat{\text{j}}\big)$

Answer

Correct option: B.

$\frac{2}{3}\big(\hat{\text{i}}+\hat{\text{j}}\big)$

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MCQ 101 Mark

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}},$ then $\vec{\text{a}}\times\vec{\text{b}}$ is:

A
$10\hat{\text{i}}+2\hat{\text{j}}+11\hat{\text{k}}$
✓
$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$
C
$10\hat{\text{i}}-3\hat{\text{j}}+11\hat{\text{k}}$
D
$10\hat{\text{i}}-2\hat{\text{j}}-10\hat{\text{k}}$

Answer

Correct option: B.

$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$

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MCQ 111 Mark

If $\vec{\text{a}}.\vec{\text{b}}=\vec{\text{a}}.\vec{\text{c}}$ and $\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{a}}\times\vec{\text{c}}.\vec{\text{a}}\neq0,$ then:

✓
$\vec{\text{b}}=\vec{\text{c}}$
B
$\vec{\text{b}}=\vec{0}$
C
$\vec{\text{b}}+\vec{\text{c}}=\vec{0}$
D
$\text{None of these}$

Answer

Correct option: A.

$\vec{\text{b}}=\vec{\text{c}}$

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MCQ 121 Mark

The value of $\big(\vec{\text{a}}\times\vec{\text{b}}\big)^2$ is:

A
$|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$
✓
$|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2-\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$
C
$|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-2\big(\vec{\text{a}}.\vec{\text{b}}\big)$
D
$|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2-\vec{\text{a}}.\vec{\text{b}}$

Answer

Correct option: B.

$|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2-\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$

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MCQ 131 Mark

If $\vec{\text{a}},\vec{\text{b}}$ represent the diagonals of a rhombus, then:

A
$\vec{\text{a}}\times\vec{\text{b}}=\vec{0}$
✓
$\vec{\text{a}}.\vec{\text{b}}=0$
C
$\vec{\text{a}}.\vec{\text{b}}=1$
D
$\vec{\text{a}}\times\vec{\text{b}}=\vec{\text{a}}$

Answer

Correct option: B.

$\vec{\text{a}}.\vec{\text{b}}=0$

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MCQ 141 Mark

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

A
$\hat{\text{i}}.\hat{\text{j}}=1$
✓
$\hat{\text{i}}.\hat{\text{i}}=1$
C
$\hat{\text{i}}\times\hat{\text{j}}=1$
D
$\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big)=1$

Answer

Correct option: B.

$\hat{\text{i}}.\hat{\text{i}}=1$

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