Embibe Experts Solutions for Chapter: Vectors, Exercise 1: MHT-CET 2019

The value of $m,$ if the vectors $\hat{i}\mathit{-}\hat{j}\mathit{-}6\hat{k}\mathit{,}\mathit{ }\hat{i}\mathit{-}3\hat{j}+4\hat{k}$ and $2\hat{i}-5\hat{j}+m\hat{k}$ are coplanar, is

If the vectors $x\hat{i}-3\hat{j}+7\hat{k}$ and $\widehat{i}+y\widehat{j}-z\widehat{k}$ are collinear then the value of $\frac{x{y}^2}{z}$ is equal

If $\overrightarrow{AB}=3\hat{ı}+5\hat{j}+4\hat{k}$, $\overrightarrow{AC}=5\hat{i}-5\hat{j}+2\hat{k}$ represent the sides of a triangle $ABC$, then the length of the median through $A$ is

If the vectors $\overrightarrow{a}=\hat{ı}-2\hat{j}+\hat{k}$, $\overrightarrow{b}=2\hat{ı}-5\hat{j}+p\hat{k}$ and $\overrightarrow{c}=5i-9\hat{j}+4\hat{k}$ are coplanar, then the value of $p$ is

If $\overrightarrow{a}=\frac{1}{\sqrt{10}}\left(3\hat{ı}+\hat{k}\right), \overrightarrow{b}=\frac{1}{7}\left(2\hat{ı}+3\hat{ȷ}-6\hat{k}\right),$ then the value of $\left(2\overrightarrow{a}-\overrightarrow{b}\right)·\left[\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left((\overrightarrow{a}+2\overrightarrow{b}\right)\right]$ is

If $\left[\begin{array}{lll}\overrightarrow{a}& \overrightarrow{b}& \overrightarrow{c}\end{array}\right]=4$, then the volume of the parallelopiped with coterminus edges $\overrightarrow{a}+2\overrightarrow{b}$, $\overrightarrow{b}+2\overrightarrow{c}, \overrightarrow{c}+2\overrightarrow{a}$ is

If $A$, $B$, $C$ and $D$ are $\left(\mathrm{3,} 7, 4\right),\left(5,-2,-3\right),\left(-\mathrm{4,} 5, 6\right)$ and $\left(\mathrm{1,} 2, 3\right)$ respectively, then the volume of the parallelepiped with $AB$, $AC$ and $AD$ as the coterminous edges, is ….cubic units.

Which of the following is not equal to $\overrightarrow{w}.\left(\overrightarrow{u}\times \overrightarrow{v}\right)$?