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

Question

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)\(\sqrt{0.39}\)

Answer 1

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=\(\sqrt{0.11}\)