Question

If A vector = icap + jcap + kcap & B vector = 4icap + 4jcap + 4kcap
& R vector = A vector + B vector then R vector makes angle with A vector is that : (1) 37° ,(2)0 , (3) 180 , (4) 45°

Answer 1

Solution:-

$\rm \: \overrightarrow{A} = \hat{i} + \hat{j} + \hat{k}$

$\rm \:\overrightarrow{ B }= 4 \hat{i} + 4\hat{j} + 4\hat{k}$

$\rm |\overrightarrow{A}| = \sqrt{ {1}^{2} + {1}^{2} + {1}^{2} } = \sqrt{3}$

$\rm |\overrightarrow{B}| = \sqrt{ {4}^{2} + {4}^{2} + {4}^{2} } = \sqrt{48} = 4 \sqrt{3}$

To find the angle

$\rm \cos\theta = \dfrac{\rm \: \overrightarrow{A} .\rm \:\overrightarrow{ B }}{AB}$

$\rm\cos\theta = \dfrac{( \hat{i} + \hat{j} + \hat{k})(4 \hat{i} + 4\hat{j} + 4\hat{k})}{4 \sqrt{3} \times \sqrt{3} }$

$\rm \: \cos\theta = \dfrac{4 + 4 + 4}{12}$

$\cos\theta = \dfrac{12}{12}$

$\cos\theta = 1$

$\theta = \cos {}^{ - 1} 1$

$\rm \: \theta = 0 \degree$

option 2 is correct

Answer 2

Explanation:

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Answer♡

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