SATHEE: Kinematics Question 146

Kinematics Question 146

Question: The unit vector parallel to the resultant of the vectors $\vec{A} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{B} = - \hat{i} + 3 \hat{j} - 8 \hat{k}$ it’s [EAMCET 2000]

Options:

A) $\frac{1}{7} (3 \hat{i} + 6 \hat{j} - 2 \hat{k})$

B) $\frac{1}{7} (3 \hat{i} + 6 \hat{j} + 2 \hat{k})$

C) $\frac{1}{49} (3 \hat{i} + 6 \hat{j} - 2 \hat{k})$

D) $\frac{1}{49} (3 \hat{i} - 6 \hat{j} + 2 \hat{k})$

Show Answer

Answer:

Correct Answer: A

Solution:

Resultant of vectors $\vec{A}$ and $\vec{B}$

$\vec{R} = \vec{A} + \vec{B} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k} - \hat{i} + 3 \hat{j} - 8 \hat{k}$

$\vec{R} = 3 \hat{i} + 6 \hat{j} - 2 \hat{k}$

$\hat{R} = \frac{\vec{R}}{| \vec{R} |} = \frac{3 \hat{i} + 6 \hat{j} - 2 \hat{k}}{\sqrt{3^{2} + 6^{2} + {(- 2)}^{2}}} = \frac{3 \hat{i} + 6 \hat{j} - 2 \hat{k}}{7}$

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Kinematics Question 146

Question: The unit vector parallel to the resultant of the vectors A→=4i^+3j^+6k^ and B→=−i^+3j^−8k^ it’s [EAMCET 2000]

Options:

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Question: The unit vector parallel to the resultant of the vectors $\vec{A} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{B} = - \hat{i} + 3 \hat{j} - 8 \hat{k}$ it’s [EAMCET 2000]