Question

Find the unit vector of 2i + 7j
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Answer 1

Answer:

(2/√53)i+(7/√53)j

Explanation:

√[(2)(2)]+[(7)(7)]

√53

(1/√53)(2i+7j)

(2/√53)i+(7/√53)j

Answer 2

$\sf{Let\ x=2\hat{i}+7\hat{j}}$

Magnitude of x =

$\sf{\sqrt{(2)^2+(7)^2} }\\\\\sf{\implies |\overrightarrow{x}|=\sqrt{4+49}=\sqrt{53} }}$

Unit vector in direction of $\sf{\overrightarrow{x}}$ =

$\sf{\hat{x}=\dfrac{\overrightarrow{x}}{|\overrightarrow{x}|} }$

$\sf{\implies \hat{x}=\dfrac{2\hat{i}+7\hat{j}}{\sqrt{53} } }$

$\sf{\implies \hat{x}=\dfrac{2\hat{i}}{\sqrt{53} } +\dfrac{7\hat{j}}{\sqrt{53} } }$

The answer is :-

$\boxed{\hat{x}=\frac{2}{\sqrt{53} }\hat{i}\ +\ \frac{7}{\sqrt{53} } \hat{j} }$