Unit Vectors

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. Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-collinear unit vectors. If $\overrightarrow{u}=\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{b}$ and $\overrightarrow{v}=\overrightarrow{a}\times \overrightarrow{b},$ then $|\overrightarrow{v}|$ is

1. $|\overrightarrow{u}|$
2. $|\overrightarrow{u}|+|\overrightarrow{u}.\overrightarrow{a}|$
3. $|\overrightarrow{u}|+|\overrightarrow{u}.\overrightarrow{b}|$
4. $|\overrightarrow{u}|+\overrightarrow{u}.(\overrightarrow{a}+\overrightarrow{b})$

Q. If the unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are inclined at an angle 2 $\theta$ such that $|\overrightarrow{a}-\overrightarrow{b}|$ <1 and 0 $\le \theta \le \pi$, then $\theta$ lies in the interval

1. $[0,\frac{\pi }{6})$
2. $(\frac{5\pi }{6},\pi ]$
3. $[\frac{\pi }{6},\frac{\pi }{2}]$
4. $[\frac{\pi }{2},\frac{\pi }{6}]$

Q. In the given figure, if $l||m$, the value of x is

1. ${205}^0$
2. ${285}^0$
3. ${75}^0$
4. None

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

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