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,
$1=\sqrt{(0.8{)}^2+(b{)}^2+(0.4{)}^2}$
$\Rightarrow 1=\sqrt{0.64+b^2+016}$
$\Rightarrow 1=0.64+b^2+0.16$
$\Rightarrow 1=0.80+b^2$
$\Rightarrow b^2=1-0.80$
$\Rightarrow b^2=02$
$\Rightarrow b=\sqrt{0.2}$