Question

given that 0.4i+0.8j+bk is the unit vector.what is the value of bgiven that 0.4i+0.8j+bk is the unit vector.what is the value of b

Answer 1

unit vector means magnitude of vector is unity .
1=root {(0.4)^2+(0.8)^2+(b)^2}
take square both side
1=0.16 +0.64 +b^2
b^2 =0.2
b=+_0.45

Answer 2

Answer:

The value of b is ±0.44

Explanation:

We have a unit vector 0.4i+0.8j+bk

We have to find the value of b in the given vector

We know that unit vector means 1

So let us equate

1=0.4i+0.8j+bk

Let us take square roots for both the sides for the above given vector

We get

$\begin{array}{l}{1^{2}=(0.4 \mathrm{i}+0.8 \mathrm{j}+\mathrm{bk})^{2}} \\ {1=0.16+0.64+\mathrm{b}^{2}} \\ {1=0.8+\mathrm{b}^{2}} \\ {1-0.8=\mathrm{b}^{2}} \\ {0.2=\mathrm{b}^{2}}\end{array}$

To find the value of b take the square root to 0.2

Hence we get  

b=√0.2

=±0.44

Hence the value of b =±0.44

(Unit vector: Unit vector is a vector where the magnitude is one)