Question

find a unit vector in the direction of vector P = 4i - 8k​

Answer 1

Answer:

$\hat P = \frac{1}{\sqrt 5} \hat i - \frac{2}{\sqrt 5} \hat k$

Explanation:

$Here, \\ \vec P= 4 \hat i - 8\hat k$

$\therefore | \vec P|=\sqrt{{4}^2+{8} ^ 2}$

$\therefore |\vec P|=\sqrt {80}$

$Now, \\ \hat P =\frac{ \vec P}{| \vec P|}$

$\therefore \hat P=\frac{ 4 \hat i +8 \hat k}{ \sqrt{80} }$

$\therefore \hat P= \frac{4 \hat i +8 \hat k}{ 4 \sqrt{5}}$

$\hat P = \frac{1}{\sqrt 5} \hat i - \frac{2}{\sqrt 5} \hat k$

Answer 2

Answer: =>1/√80 x (4j-8k)

Explanation:

vector P = 4j - 8k

Magnitude of P = |P| = √[(4x4) + (8x8)] = √80

now, unit vector of P = P/|P|

         =>1/√80 x (4j-8k)   = answer :)