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Work Energy And Power NEET Questions — Free MCQ Practice

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$\vec{A} = \hat{i} + \hat{j} - \hat{k}; \vec{B} = 2 \hat{i} + 3 \hat{j} + 5 \hat{k}$ angle between $\vec{A}$ and $\vec{B}$ is

A.

$120 °$

B.

$90 °$

C.

$60 °$

D.

$30 °$

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Explanation

Angle between two vectors = $\cos^{- 1} [\frac{\vec{A} . \vec{B}}{A B}]$

$= \cos^{- 1} [\frac{2 + 3 - 5}{\sqrt{3} \times \sqrt{38}}] = \cos^{- 1} (0) = 90 °$

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Given the vectors

$\vec{A} = 2 \hat{i} + 3 \hat{j} - \hat{k} \vec{B} = 3 \hat{i} - 2 \hat{j} - 2 \hat{k} & \vec{C} = p \hat{i} + p \hat{j} + 2 p \hat{k}$

Find the angle between $(\vec{A} - \vec{B}) & \vec{C}$

A.

$θ = \cos^{- 1} (\frac{2}{\sqrt{3}})$

B.

$θ = \cos^{- 1} (\frac{\sqrt{3}}{2})$

C.

$θ = \cos^{- 1} (\frac{\sqrt{2}}{3})$

D.

none of these

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Explanation

(C)

$\vec{A} - \vec{B} = (2 \hat{i} + 3 \hat{j} - \hat{k}) - (3 \hat{i} - 2 \hat{j} - 2 \hat{k}) = - \hat{i} + 5 \hat{j} + \hat{k} Let \vec{A} - \vec{B} = \vec{D} (let) ∴ \vec{D} = - \hat{i} + 5 \hat{j} + \hat{k} |\vec{D}| = \sqrt{{(- 1)}^{2} + {(5)}^{2} + {(1)}^{2}} = \sqrt{27} To find the angle between \vec{D} & \vec{C} |\vec{C}| = \sqrt{{(p)}^{2} + {(p)}^{2} + {(2 p)}^{2}} = P \sqrt{6} \vec{D} . \vec{C} = DC cosθ (- \hat{i} + 5 \hat{j} + \hat{k}) . (p \hat{i} + p \hat{j} + 2 p \hat{k}) = \sqrt{27} \times p \sqrt{6} cosθ - p + 5 p + 2 p = p \sqrt{27 \times 6} cosθ 6 = \sqrt{27 \times 6} cosθ cosθ = \sqrt{\frac{6}{27}} = \sqrt{\frac{2}{9}} cosθ = \frac{\sqrt{2}}{3} or θ = \cos^{- 1} \frac{\sqrt{2}}{3}$

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The vector having a magnitude of 10 and perpendicular to the vector $3 \hat{i} - 4 \hat{j}$ is

A.

$4 \hat{i} + 3 \hat{j}$

B.

$5 \sqrt{2} \hat{i} - 5 \sqrt{2} \hat{j}$

C.

$8 \hat{i} + 6 \hat{j}$

D.

$8 \hat{i} - 6 \hat{j}$

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Explanation

$(3 i + 4 j) . (8 i + 6 j) = 0$

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A force $\vec{F} = 3 \hat{i} + c \hat{j} + 2 \hat{k}$ acting on a particle causes a displacement $\vec{d} = - 4 \hat{i} + 2 \hat{j} + 3 \hat{k}$ . If the work done is 6J then the value of 'c' is

A.

12

B.

0

C.

6

D.

1

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Explanation

$W = \vec{F} . \vec{d} \Rightarrow 6 = \vec{F} . \vec{d} \Rightarrow 6 = - 12 + 2 C + 6 \Rightarrow C = 6$

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A vector that is perpendicular to both the vectors $\vec{a} = \hat{i} - 2 \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$ is

A.

$- \hat{i} + \hat{k}$

B.

$- \hat{i} - 2 \hat{j} + \hat{k}$

C.

$\hat{i} - 2 \hat{j} + \hat{k}$

D.

$\hat{i} + \hat{k}$

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Explanation

(A)

$\hat{i} + \hat{k} = - \hat{i} + 0 \hat{j} + \hat{k} \vec{a} . (- \hat{i} + \hat{k}) = - 1 + 0 + 1 = 0 \vec{b} . (- \hat{i} + \hat{k}) = - 1 + 0 + 1 = 0$

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If $θ$ is the angle between vectors $\vec{a}$ and $\vec{b}$ , and $| \vec{a} \times \vec{b} | = \vec{a} . \vec{b}$ , then $θ$ is equal to

A.

$0 °$

B.

$180 °$

C.

$135 °$

D.

$45 °$

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Explanation

$G i v e n, | \vec{a} \times \vec{b} | = \vec{a} . \vec{b} \Rightarrow a b \sin θ = a b \cos θ \Rightarrow \tan θ = 1 \Rightarrow θ = 45 °$

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The vector $\vec{b}$ , which is collinear with the vector $\vec{a}$ =(2, 1, -1) and satisfies the condition $\vec{a}$ . $\vec{b}$ =3, is

A.

(1, 1/2, -1/2)

B.

(2/3, 1/3, -1/3)

C.

(1/2, 1/4, -1/4)

D.

(1, 1, 0)

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Explanation

$Going through the options; Only (A) satifies the condition \vec{a} . \vec{b} = 3 .$

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If $3 \hat{i} + 2 \hat{j} + 8 \hat{k}$ and $2 \hat{i} + x \hat{j} + \hat{k}$ are at right angle then x=

A.

7

B.

-7

C.

5

D.

-4

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Explanation

If two vectors are at right angle, then their dot product = 0

$\Rightarrow (3 \hat{i} + 2 \hat{j} + 8 \hat{k}) . (2 \hat{i} + x \hat{j} + \hat{k}) = 0 \Rightarrow 6 + 2 x + 8 = 0 \Rightarrow x = - 7$

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If a, b, c are three non-zero vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$ the value of $\vec{a} . \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}$ is

A.

Less than zero

B.

equal to zero

C.

greater than zero

D.

3

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Let $α, β, γ$ be distinct real numbers. The points with position vectors $α \hat{i} + β \hat{j} + γ \hat{k}, β \hat{i} + γ \hat{j} + α \hat{k}, γ \hat{i} + α \hat{j} + β \hat{k}$

A.

are collinear

B.

from an equilateral triangle

C.

form an isosceles triangle

D.

from a right angled triangle

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Work Energy And Power MCQs for NEET — Physics Questions with Answers

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