Unit Vectors

Q. If a, b and c are unit vectors, then $|a-b{|}^2+|b-c{|}^2+|c-a{|}^2$ does not exceed

1. 4
2. 9
3. 8
4. 6

Q.

Given $\overrightarrow{A}=0.3\hat{i}+0.4\hat{j}+c\hat{k}$. Calculate the value of c if A is a unit vector.

1. 0.75

2. 0.87

3. 0.96

4. 0.45

Q. If a, b and c are unit vectors, then $|a-b{|}^2+|b-c{|}^2+|c-a{|}^2$ does not exceed

1. 4
2. 9
3. 8
4. 6

Q. A unit vector $\overrightarrow{a}$ makes an angle of $45°$ with positive $z-$axis and if $\overrightarrow{a}+\hat{i}+\hat{j}$ is a unit vector, then $\overrightarrow{a}=$

1. $(-\frac{1}{2},-\frac{1}{2},\frac{1}{\sqrt{2}})$
2. $(\frac{1}{2},-\frac{1}{2},\frac{1}{\sqrt{2}})$
3. $(\frac{1}{2},\frac{1}{2},\frac{1}{\sqrt{2}})$
4. $(-\frac{1}{2},-\frac{1}{2},-\frac{1}{\sqrt{2}})$