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Question

Write a vector of magnitude $$ 9 $$ units in the direction of vector $$ -2 \hat {i} + \hat {j} + 2 \hat {k}  $$ 


Solution

Let $$ \overrightarrow {a} = -2 \overrightarrow {i} + \overrightarrow {j} + 2 \overrightarrow {k} $$
Required vector $$ \frac { \overrightarrow {a} }{ | \overrightarrow {a} | } \times 9 $$
$$ = \frac { 9( -2 \overrightarrow {i} + \overrightarrow {j} + 2 \overrightarrow {k}) }{ \sqrt { 4 + 1+4 } } = \frac { 9 ( -2 \overrightarrow {i} +\overrightarrow {j}+ 2 \overrightarrow {k} )}{3} $$
$$ =-6 \overrightarrow {i} + 3 \overrightarrow {j} + 6 \overrightarrow {k} $$

Physics

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