R D Sharma Solutions for Chapter: Scalar or Dot Product, Exercise 4: MULTIPLE CHOICE QUESTIONS (MCQs)

If $\overrightarrow{a}$ is a non-zero vector of magnitude $\text{'}a\text{'}$ and $\lambda$ is a non-zero scalar, then $\lambda \overrightarrow{a}$ is a unit vector if

The values of $x$ for which the angle between $\overrightarrow{a}=2x^2\hat{i}+4x\hat{j}+\hat{k},\overrightarrow{b}=7\hat{i}-2\hat{j}+x\hat{k}$ is obtuse and the angle between $\overrightarrow{b}$ and the $z$ -axis is acute and less than $\frac{\pi }{6}$ are

If the angle between the vectors $x\hat{i}+3\hat{j}-7\hat{k}$ and $x\hat{i}-x\hat{j}+4\hat{k}$ is acute, then $x$ lies in the interval

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors inclined at an angle $\theta$, such that $\left|\overrightarrow{a}+\overrightarrow{b}\right|<1,$ then

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three unit vectors, such that $\left|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\right|=1$ and $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$ If $\overrightarrow{c}$ makes angles $\alpha$ and $\beta$ with $\overrightarrow{a}$ and $\overrightarrow{b}$ respectively, then $\cos \alpha +\cos \beta =$

The orthogonal projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ is

If $\theta$ is an acute angle and the vector $(\sin \theta )\hat{i}+(\cos \theta )\hat{j}$ is perpendicular to the vector $\hat{i}-\sqrt{3}\hat{j},$ then $\theta =$

If$\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors and $\theta$ the angle between them, then $\overrightarrow{a}+\overrightarrow{b}$ is a unit vector if $\theta =$