# If a unit vector is represented by 0.5i +0.8 j ​+ck then the value of 'c' is

If a unit vector is represented by  $$0.5\hat{i} +0.8\hat{ j} ​+c\hat{k}$$  then the value of 'c' is

a)$$\sqrt{0.01}$$

b)$$\sqrt{0.11}$$

c)$$1$$

d)$$\sqrt{0.39}$$

verified

Correct option is b) $$\sqrt{0.11}$$

Explaination::

The unit vector is given as $$\hat{A}=0.5\hat{i} +0.8\hat{ j} ​+c\hat{k}$$

Magnitude of unit vector is always equal to 1

$$\sqrt{(0.5)^2 +(0.8)^2 ​+(c)^2}=1$$

$$\therefore 0.25+0.64+c^2=1$$

c2=1-0.89

c=$$\sqrt{0.11}$$