Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 15: Exercise (Analytical Questions)

The angle between the vectors $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$ and $\left(\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$ is,

The vector $\overrightarrow{P}=a\hat{\mathrm{i}}+a\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $\overrightarrow{Q}=a\hat{\mathrm{i}}-2\hat{\mathrm{j}}-\hat{\mathrm{k}}$ are perpendicular to each other. The positive value of $a$ is,

What is the projection of $\left(3 \hat{i}+4 \hat{k}\right)$ on the $\mathrm{Y}$-axis?

If $\overrightarrow{\mathrm{A}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$ and $A$ and $B$ are the magnitudes of $\overrightarrow{A}$ and $\overrightarrow{B}$, then which of the following is not true?

A vector $\overrightarrow{F_1}$ is along the positive $X$-axis. If its vector product with another vector $\overrightarrow{F_2}$ is zero then $\overrightarrow{F_2}$ maybe:

If  $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and  $\hat{\mathrm{k}}$ are unit vectors along $X,Y$ and $Z$ axis respectively, then tick the wrong statement:

Two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ are inclined to each other at angle $\mathrm{\theta }$. Which of the following is the unit vector, perpendicular to $\overrightarrow{P}$ and $\overrightarrow{Q}$?

The magnitude of the vector product of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ may not be :