Question

Find the unit vector of 4i cap -3j cap+ k cap​

Answer 1

Solution :

➡ Given:

✏ A physical quantity is represented by $\rm \: \vec{A} = 4\hat{i} - 3\hat{j} + \hat{k}$

➡ To Find :

✏ Unit vector of given physical quantity.

➡ Formula :

✏ Unit vector is given by

$\star \: \underline{ \boxed{ \bold{ \rm{ \pink{ \hat{A} = \frac{ \vec{A}}{ | \vec{A}| } }}}}} \: \star$

➡ Terms indication:

✏ $\hat{A}$ denotes unit vector.

✏ $\vec{A}$ denotes vector form of physical quantity.

✏ $|\vec{A}|$ denotes magnitude of physical quantity.

➡ Calculation:

$\mapsto \rm | \vec{A}| = \sqrt{ {4}^{2} + {3}^{2} + {1}^{2} } \\ \\ \mapsto \rm \red{ | \vec{A}| = \sqrt{26} \: unit} \\ \\ \mapsto \rm \: \hat{A} = \frac{ \vec{A}}{ | \vec{A}| } \\ \\ \mapsto \underline{ \boxed{ \bold{ \rm{ \purple{ \hat{A} = \frac{4 \hat{i} - 3 \hat{j} + \hat{k}}{ \sqrt{26} } }}}}} \: \orange{ \bold{ \star}}$

➡ Additional information:

✏ The latin word vector means Carrier.

✏ Vector quantity has both magnitude as well as direction.

Answer 2

$\mathtt{\huge{\fbox{Solution :)}}}$

Given ,

The vector is $\sf 4 \hat{ \imath} - 3\hat{ \jmath} + \hat{ k}$

We know that , the unit vector is defined as the vector divided by its magnitude

$\mathtt{\large{ \fbox{ Unit \: vector = \frac{ \vec{a}}{ | \vec{a}| } }}}$

Thus ,

$\sf \hookrightarrow Unit \: vector = \frac{4 \hat{ \imath} - 3\hat{ \jmath} + \hat{ k}}{ \sqrt{ {(4)}^{2} + {( - 3)}^{2} + {(1)}^{2} } } \\ \\\sf \hookrightarrow Unit \: vector = \frac{4 \hat{ \imath} - 3\hat{ \jmath} + \hat{ k}}{ \sqrt{ 16 + 9 + 1 } } \\ \\\sf \hookrightarrow Unit \: vector = \frac{4 \hat{ \imath} - 3\hat{ \jmath} + \hat{ k}}{ \sqrt{ 26 } }$

Hence , the unit vector is $\mathtt{ \fbox{\frac{4 \hat{ \imath} - 3\hat{ \jmath} + \hat{ k}}{ \sqrt{ 26 } } }}$

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