Question

Calculate the scalar product of the following vectors.
Find the vector b being given that it satisfies the following conditions: the scalar product $b\cdot c=3,wherec=\{1,-1,2\},$ the vector b is perpendicular to $a$ and $d$, where $a=\{-2,-1,1\}andd=\{3,5,-2\}.$

Answer 1

let $\overrightarrow{b}=x\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}$

$b.c=x-y+2z=\mathrm{3........}\left(1\right)$

$a.b=-2x-y+z=\mathrm{0........}\left(2\right)$

$b.d=3x+5y-2z=\mathrm{0.......}\left(3\right)$

Equation $2\left(2\right)+\left(3\right)$,We get

$x=3z$

Substituting value of z in equation (1) and (2)

$5z-y=\mathrm{3..........}\left(4\right)$

$-5z-y=\mathrm{0.......}\left(5\right)$

$y=-\frac{3}{2}$

$z=\frac{3}{10}$

$x=\frac{9}{10}$