Question

Solve this question. Best explanation will be marked as brainliest.​

Answer 1

Answer:

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Answer 2

Explanation:

Given -

• $\vec\mathsf {A = 3 \hat{i} + 2 \hat{j} \: and \: B = 2 \hat{i} + 3 \hat{j} - \hat{k}}$

To Find -

• $\mathsf{A \: unit \: vector \: along \: \vec{A} - \vec{B} }$

Now,

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

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

$\mathsf{ \vec{A} - \vec{ B} = \hat{i} - \hat{j} + \hat{k} }$

$\mathsf{ magnitude \: of \: \vec{A} - \vec{ B} = \sqrt{(1) {}^{2} + ( - 1) {}^{2} + (1) {}^{2} } }$

$\mathsf{ magnitude \: of \: \vec{A} - \vec{ B} = \sqrt{3} }$

Now,

$\mathsf{Unit \: vector \: along \: \vec{A} - \vec{ B} = \frac{ \vec{A } - \vec{B}}{ | \vec{A} + \vec{B}| } }$

$\mathsf{\frac{ \hat{i} - \hat{j} + \hat{k}}{ \sqrt{3} } }$

$\mathsf{ \implies \frac{1}{ \sqrt{ 3} } ( \hat{i} - \hat{j} + \hat{k})}$