Question

h) Find a vector of magnitude 4 units in the direction of the vector 2î - j +2k^​

Answer 1

Step-by-step explanation:

$Let \: \: \vec{a} = 2 \hat{i} - \hat{j} + 2\hat{k}$

Now,

$\hat{a} = \frac{2 \hat{i} - \hat{j} + 2\hat{k}}{ \sqrt{ {(2)}^{2} + {( - 1)}^{2} + {(2)}^{2} } }$

$\implies \hat{a} = \frac{2 \hat{i} - \hat{j} + 2\hat{k}}{ \sqrt{ {4 + 1 + 4 } }}$

$\implies \hat{a} = \frac{2 \hat{i} - \hat{j} + 2\hat{k}}{ \sqrt{ 9 }}$

$\implies \hat{a} = \frac{2 \hat{i} - \hat{j} + 2\hat{k}}{3}$

$\implies \hat{a} = \frac{2}{3} \hat{i} - \frac{1}{3} \hat{j} + \frac{2}{3} \hat{k}$

Required vector

$\implies \vec{b} = 4\hat{a} = \frac{8}{3} \hat{i} - \frac{4}{3} \hat{j} + \frac{8}{3} \hat{k}$