Question

A unit vector is represented as $(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k}).$ Hence the value of ‘b’ must be

• A. 0.4
• B. $\sqrt{0.6}$
• C. 0.2
• D. $\sqrt{0.2}$

Answer 1

Answer: (D)

Given, unit vector $=0.8 \hat{ i }+b \hat{ j }+ 0 \cdot 4 \hat{ k }$
Magnitude of vector $(A)=\sqrt{x^{2}+y^{2}+z^{2}}$
Hëre, $x=0.8, y=b, z=0.4$
Now,
$1=\sqrt{(0.8)^{2}+(b)^{2}+(0.4)^{2}}$
$\Rightarrow 1=\sqrt{0.64+b^{2}+016}$
$\Rightarrow 1=0.64+b^{2}+0.16$
$\Rightarrow 1=0.80+b^{2} $
$\Rightarrow b^{2}=1-0.80 $
$ \Rightarrow b^{2} =02 $
$\Rightarrow b =\sqrt{0. 2}$