Vectors

Let $\vec{A}$ and $\vec{B}$ are two non-zero vectors of different magnitude. Which one of the following is the correct equation ?

Which of the following is not a vector quantity?

Find the magnitude of 3 $i$ + 2 $j$ + $k$.

If the angle between the vectors $\vec{A}$ and $\vec{B}$ is $\theta$, the value of the product $(\vec{B}\times\vec{A})\cdot\vec{A}$ is equal to

The magnitude of the $x$-component of vector $\vec{A}$ is 3 and the magnitude of vector $\vec{A}$ is 5. What is the magnitude of the $y$-component of vector $\vec{A}$ ?

Let $\vec{A}=\dfrac{1}{\sqrt{2}}\cos\theta\overset{\hat{}}{i}+\dfrac{1}{\sqrt{2}}\sin\theta\overset{\hat{}}{j}$ be any vector. What will be the unit vector $\overset{\hat{}}{n}$ in the direction of $\vec{A}$ ?

Which of the following pairs of vectors are parallel?

Let $\vec{P}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{Q}=-(\hat{i}+\hat{j}+\hat{k})$. The angle between $(\vec{P}-\vec{Q})$ and $\vec{P}$ is

The angle made by vector $\vec{A}=2 \hat{i}+3 \hat{j}$ with x-axis and that with y-axis are respectively.

If a unit vector is represented by $\vec{U}=0.9 \hat{i}-0.2 \hat{j}+m \hat{k}^{\prime}$, then the value of m is

The condition that $(\vec{a}\cdot\vec{b})^{2}=\left( a^{2}b^{2} \right)$ is satisfied when

If the sum $\vec{A}+\vec{B}$ of two vectors $A$ and $B$ equals the difference $\vec{A}-\vec{B}$ between them, then

If $\vec{A}=5\overset{\hat{}}{i}+7\overset{\hat{}}{j}-3\overset{\hat{}}{k}$ and $\vec{B}=2\overset{\hat{}}{i}+2\overset{\hat{}}{j}-c\overset{\hat{}}{k}$ are perpendicular vectors, the value of $c$ is

There are two vectors $\vec{A}=6 \hat{i}+9 \hat{j}-\hat{k}$ and $\vec{B}=2 \hat{i}+3 \hat{j}-p \hat{k}$ which have the same direction. The value of ' p ' is

If two vectors $\vec{A}=4 \hat{i}+n \hat{j}+2 \hat{k}$ and $\vec{B}=2 \hat{i}+2 \hat{j}-\hat{k}$ are mutually perpendicular to each other then value of ' n ' is