Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: AP EAPCET 2021 (19-Aug Afternoon)

If $\hat{i}+4\hat{j}+3\hat{k},\hat{i}+2\hat{j}+3\hat{k},3\hat{i}+2\hat{j}+\hat{k}$ are position vectors of $A,B,C$ respectively and if $D,E$ are mid points of sides $BC$ and $AC$, then $\overrightarrow{DE}$ is equal to

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\frac{\overrightarrow{a}·\overrightarrow{b}}{\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|}<0$ and $|\overrightarrow{a}·\overrightarrow{b}|=|\overrightarrow{a}\times \overrightarrow{b}|$, then the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Let $x, y$ are real numbers. If $\overrightarrow{a}=\left(\sin x\right)\hat{i}+\left(\sin y\right)\hat{j}$ and $\overrightarrow{b}=\left(\cos x\right)\hat{i}+\left(\cos y\right)\hat{j}$, then $|\overrightarrow{a}\times \overrightarrow{b}|$ is

If the projections of the line segment $\overrightarrow{AB}$ on $XY, YZ$ and $ZX$ planes are $\sqrt{15},\sqrt{46},7$ respectively, then the projection of $\overrightarrow{AB}$ on $y-$axis is

Let $\overrightarrow{u}$ and $\overrightarrow{v}$ be two non-zero vectors with the intermediate angle $45°$. Then $|\overrightarrow{u}\times \overrightarrow{v}|=$

Given $\overrightarrow{a}=3\hat{i}-\hat{j},\overrightarrow{b}=2\hat{i}+\hat{j}-3\hat{k}$ and $\overrightarrow{b}=\overrightarrow{b_1}+\overrightarrow{b_2}$, where $\overrightarrow{b_1}$ is parallel to $\overrightarrow{a}$ and $\overrightarrow{b_2}$ is perpendicular to $\overrightarrow{a}$ then $\overrightarrow{b_2}$ is equal to

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three-unit vectors and $\overrightarrow{a}·\overrightarrow{b}=\overrightarrow{a}·\overrightarrow{c}=0$. If the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi }{3}$, then $[\overrightarrow{a} \overrightarrow{b} \overrightarrow{c}{]}^2=$

The equation of the plane passing through $3 \hat{i}+2 \hat{j} +6 \hat{k}$ and parallel to the vectors $2 \hat{i}+ \hat{j}+ \hat{k}$ and $i-j+k$ is