Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 2: Exercise-2

Assertion : A vector is a quantity that has both magnitude and direction and obeys the triangle law of addition.

Reason : The magnitude of the resultant vector of two given vectors can never be less than the magnitude of any of the given vector.

Assertion : If the rectangular components of a force are $8 N$ and $6 N,$ then the magnitude of the force is $10 N.$

 Reason : If $\left|\overrightarrow{\Delta }\right|\left|\overrightarrow{B}\right|{=}_1$ then ${\left|{\overrightarrow{A}}^{\times }\overrightarrow{B}\right|}^2+{\left|\overrightarrow{A·B}\right|}^2=1.$

Assertion : If three vectors $\overrightarrow{A, B}$ and $\overrightarrow{C}$ satisfy the relation $\overrightarrow{A.B}=0 \overrightarrow{A.C}=0$ then the vector $\overrightarrow{\Lambda }$ is paraliel to $\overrightarrow{B}\times \overrightarrow{C}.$
Reason : $\overrightarrow{A}\perp \overrightarrow{B}$ and $\overrightarrow{A}\perp \overrightarrow{C}$ hence $\overrightarrow{A}$ is perpendicular to plane formed by $\overrightarrow{B}$ and $\overrightarrow{C}.$

Find the resultant of the three vectors $\overrightarrow{OA}, \overrightarrow{OB}$ and $\overrightarrow{OC}$ each of magnitude as shown in figure?

A vector $\overrightarrow{A}$ points vertically downward $\&$ $\overrightarrow{B}$ points towards east, then the vector product $\overrightarrow{A}\times \overrightarrow{B}$ is

Which of the arrangement of axes in Fig. can be labelled "right-handed. coordinate system"? As usual, each axis label indicates the positive side of the axis.

The unit vector perpendicular to each of the vectors $3\hat{i}+\hat{j}+2\hat{k}$ and $2\hat{i}-2\hat{j}+\hat{k}$ is given by

Three vectors $\overrightarrow{A},\overrightarrow{ B}$ and $\overrightarrow{C}$ are such that $\overrightarrow{A}=\overrightarrow{B}+\overrightarrow{C}$ and their magnitudes are in ratio $5: 4: 3$ respectively:
Find angle between vector $\overrightarrow{A}$ and $\overrightarrow{C}$