Question 11 MarkA vector whose initial and terminal points coincide, is called __________ .AnswerZero vector.View full question & answer→
Question 21 MarkIf $\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k}$, then the value of $|\vec{a} \times \vec{b}|$ will be ___________ .Answer$\sqrt{507}$View full question & answer→
Question 31 MarkThe area of triangle ABC will be __________ .Answer$\frac{1}{2}|\vec{a} \times \vec{b}|$View full question & answer→
Question 41 MarkIf $\vec{a}$ and $\vec{b}$ are two non-zero vactors and $\vec{a} \times \vec{b}=0$ if and only if $\vec{a}$ and $\vec{b}$ are. ___________ .Answerparallel to each otherView full question & answer→
Question 51 MarkIf $\vec{a}$ is a unit vector and $(\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=15$, then the value of $|\vec{x}|$ will be __________ .Answer4View full question & answer→
Question 61 MarkIf the angle between two non-zero vectors $\vec{a}$ and $\vec{b}$ is $\theta$, then $\cos \theta=$ ___________ .Answer$\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}$View full question & answer→
Question 71 Mark$\hat{i} \cdot \hat{j}=\hat{j} \cdot \hat{k}=\hat{k} \cdot \hat{i}=$ ___________ .AnswerZeroView full question & answer→
Question 81 MarkSuppose that $\vec{a}$ and $\vec{b}$ are two non-zero vectors. Then $\vec{a} \cdot \vec{b}=0$ if and only if ____________ .Answer$\vec{a}$ and $\vec{b}$ are mutually perpendicular.View full question & answer→
Question 91 MarkDirection cosines of vector $\vec{a}=\hat{i}+\hat{j}-2 \hat{k}$ will be ___________ .Answer$\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}$View full question & answer→
Question 101 MarkTwo vectors $\vec{a}$ and $\vec{b}$ are called equal vectors if their ___________ .Answermagnitudes and directions are the same.View full question & answer→
Question 111 MarkThe numbers $l r, m r$ and $n r$ proportional to direction cosines are called __________ of $\vec{r}$.Answerdirection ratiosView full question & answer→