Question

# If $\stackrel{\to }{a,}\stackrel{\to }{b,}\stackrel{\to }{c}$are three non-coplanar vectors, such that $\stackrel{\to }{d}·\stackrel{\to }{a}=\stackrel{\to }{d}·\stackrel{\to }{b}=\stackrel{\to }{d}·\stackrel{\to }{c}=0,$ then show that $\stackrel{\to }{d}$ is the null vector.

Open in App
Solution

## Given that: $\stackrel{\to }{d}·\stackrel{\to }{a}=0$ so, either $\stackrel{\to }{d}$ = 0 or $\stackrel{\to }{d}\perp \stackrel{\to }{a}$ similarly, $\stackrel{\to }{d}·\stackrel{\to }{b}=0$ so, $\stackrel{\to }{d}$ = 0 or $\stackrel{\to }{d}\perp \stackrel{\to }{b}$ Also, $\stackrel{\to }{d}·\stackrel{\to }{c}=0$ so, $\stackrel{\to }{d}$ = 0 or $\stackrel{\to }{d}\perp \stackrel{\to }{c}$ But $\stackrel{\to }{d}$ cannot be perpendicular to $\stackrel{\to }{a},\stackrel{\to }{b},\stackrel{\to }{c}$ as $\stackrel{\to }{a},\stackrel{\to }{b},\stackrel{\to }{c}$ are non-coplanar. so, $\stackrel{\to }{d}$=0. $\stackrel{\to }{d}$ is a null vector.

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos