SATHEE: Motion in a Plane - Result Question 11

Motion in a Plane - Result Question 11

13. The angle between the two vectors $\vec{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$ and $\vec{B} = 3 \hat{i} + 4 \hat{j} - 5 \hat{k}$ will be

(a) zero

(b) $45^{\circ}$

(c) $90^{\circ}$

(d) $180^{\circ}$

[2001, 1994]

Show Answer

Answer:

Correct Answer: 13. (c)

Solution:

(c) $\vec{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}, \vec{B} = 3 \hat{i} + 4 \hat{j} - 5 \hat{k}$

$\vec{A} \cdot \vec{B} = (3 \hat{i} + 4 \hat{j} + 5 \hat{k}) \cdot (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$

$| \vec{A} | | \vec{B} | \cos θ = 9 + 16 - 25 = 0$

$| \vec{A} | \neq 0, | \vec{B} | \neq 0$ , hence, $\cos θ = 0, θ = 90^{\circ}$

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