Embibe Experts Solutions for Exercise 6: Assignment Set-2

If $\left[\right(2\overrightarrow{a}+\overrightarrow{b}\left)\overrightarrow{c}\overrightarrow{d}\right]=\lambda \left[\overrightarrow{a}\overrightarrow{c}\overrightarrow{d}\right]+\mu \left[\overrightarrow{b}\overrightarrow{c}\overrightarrow{d}\right]$ then $\lambda +\mu$ is equal to

If $\overrightarrow{p}=2\overrightarrow{a}-3\overrightarrow{b},\overrightarrow{q}=\overrightarrow{a}-2\overrightarrow{b}+\overrightarrow{c},\overrightarrow{r}=-3\overrightarrow{a}+\overrightarrow{b}+2\overrightarrow{c},\overrightarrow{a},$ $\overrightarrow{b},\overrightarrow{c}$ being non-zero, non-coplanar vectors, then $-2\overrightarrow{a}+3\overrightarrow{b}-\overrightarrow{c}$ is equal to

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non-coplanar vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\alpha \overrightarrow{d}$ and $\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=\beta \overrightarrow{a}$ then $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}$ is equal to

The position vector of three points are $2\overrightarrow{a}-\overrightarrow{b}+3\overrightarrow{c}, \overrightarrow{a}-2\overrightarrow{b}+\lambda \overrightarrow{c}$ and $\mu \overrightarrow{a}-5\overrightarrow{b}$ where $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non coplanar vectors. The points are collinear when

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors such that $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|=\left|\overrightarrow{c}\right|=6$ and angle between $\overrightarrow{a}$ and $\overrightarrow{b}, \overrightarrow{b}$ and $\overrightarrow{c}$ and $\overrightarrow{c}$ and $\overrightarrow{a}$ is $\frac{\pi }{3}$ each then the volume of the triangular prism whose adjacent edges are represented by vectors $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ is $\sqrt{2}v$ then $v$ is equal to

Let $\overrightarrow{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{b}$ be another vector such that $\overrightarrow{a}·\overrightarrow{b}=14$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+\hat{j}-8\hat{k},$ then $\overrightarrow{b}=b_1\hat{i}+\hat{j}+b_2\hat{k}$ then $\left(b_1^{b_2}\right)$ is equal to

$P$ be any point on the circumcircle of the equilateral triangle of side length $6$ units, then the value of $|\overrightarrow{PA}{|}^2+|\overrightarrow{PB}{|}^2+|\overrightarrow{PC}{|}^2$ is equal to

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=10$ then the value of $[2\overrightarrow{a}-\overrightarrow{b} 3\overrightarrow{b}-\overrightarrow{c} 2\overrightarrow{c}-\overrightarrow{a}]$ is equal to