SATHEE: Kinematics Question 439

Kinematics Question 439

Question: Obtain the directions of vector $(\vec{A} - \vec{B}),$ if $\vec{A} = 2 \hat{i} + 3 \hat{j} = \hat{k}, \vec{B} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$

Options:

A) $0, \frac{1}{\sqrt{5}}, \frac{- 2}{\sqrt{5}}$

B) $0, \frac{1}{\sqrt{5}}, \frac{1}{\sqrt{5}}$

C) 0, 0, $\frac{1}{\sqrt{5}}$

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $(\vec{A} - \vec{B}) = \sqrt{1 + 4} = \sqrt{5}$

$(\vec{A} - \vec{B}) = 2 \hat{i} + 3 \hat{j} + \hat{k} - 2 \hat{i} - 2 \hat{j} - 3 \hat{k}$ $= \hat{j} - 2 \hat{k}$

$| \vec{A} - \vec{B} | = \sqrt{1 + 4} = \sqrt{5}$

Direction cosine $= \frac{0}{\sqrt{5}}, \frac{1}{\sqrt{5}}, - \frac{2}{\sqrt{5}}$ i.e., $= 0, \frac{1}{\sqrt{5}}, - \frac{2}{\sqrt{5}}$ .

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