Question

Let, $a=i-j+2k$. Then the vector in the direction of a with magnitude $5$ units is ?

• A. $5i-5j+10k$
• B. $-5i-5j+10k$
• C. $\dfrac{1}{√6}[5i-5j+10k]$
• D. $\dfrac{1}{√6}[10i-5j+5k]$

Answer 1

Answer: (C)

$\dfrac{1}{√6}[5i-5j+10k]$

Answer 2

Given that

$a =i-j+2k$

Then, first find magnitude of $a$

$|a|=√(1^{2}+(-1)^{2}+2^{2})$

  $=√6$

Then the unit vector in the direction of a is

$=$  $\dfrac{1}{√6}[i-j+2k]$

as per the question the vector having a magnitude of 5

$=$$\dfrac{1}{√6}[5i-5j+10k]$  (Ans.)