Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: COMEDK UGET 2014

Given two vectors $\hat{\mathit{i}}\mathit{-}\hat{\mathit{j}}$ and $\hat{i}\mathit{-}2\hat{j}$. The unit vector, coplanar with the two given vectors and perpendicular to $(i-j)$ is

If $a, b, c$ are three-zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of $|\mathrm{a}+\mathrm{b}+\mathrm{c}{|}^2$ is

The sin of the angle between the vectors $3\hat{i}+\hat{j}+2\hat{k}$ and $\hat{i}+\hat{j}+2\hat{k}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors of magnitude $2$ and inclined at an angle $60°$, then angle between $\overrightarrow{a}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

The direction ratios of the line which is perpendicular to lines $\frac{x-1}{2}=\frac{y+17}{-3}=\frac{z-6}{1}$ and $\frac{x+5}{1}=\frac{y+3}{2}=\frac{z-4}{-2}$ are