Question

If a unit vector is represented by 2i + 5j + ck. Then c is:

(a) -27 (b) -28 (c) 27 (d) 28​

Answer 1

Given:

A unit vector $2i + 5j+ ck$

To Find:

Value of c =?

Step-by-step explanation:

If a unit vector is A = $ai + bj+ ck$

Then, |A| = $\sqrt{a^{2} + b^{2} + c^{2} }$

Let, V = $2i + 5j+ ck$

The magnitude of the unit vector always equals to 1

i.e. |V| = 1

|V| = $\sqrt{2^{2} + 5^{2} + c^{2} }$ = 1  ------- (1)

On squaring both sides of the equation (1)

${2^{2} + 5^{2} + c^{2} }$ = 1

$4 + 25 + c^{2} = 1$

$29 + c^{2} = 1$

$c = \sqrt{-28}$

Hence, the value of c is $c = \sqrt{-28}$