Question

Determine the possible value(s) of h if the vectors u = -2i+hj+h+ 4)k and v = hi+ 3j+hk are perpendicular.

Answer 1

The vectors are perpendicular for:

1) h = 0

2) h = -5

Explanation:

For two vectors to be perpendicular the dot product of the 2 vectors should be zero

The given vectors are

`\overrightarrow{v_(1)}=-2\widehat{i}+h\widehat{j}+(h+4)\widehat{k}\\\\\overrightarrow{v_(2)}=h\widehat{i}+3\widehat{j}+h\widehat{k}`

The dot product is calculated as

`\overrightarrow{v_(1)}\cdot \overrightarrow{v_(2)}=(-2\widehat{i}+h\widehat{j}+(h+4)\widehat{k})\cdot (h\widehat{i}+3\widehat{j}+h\widehat{k})\\\\\therefore 0=(-2h+3h+h^(2)+4h)\\\\h^(2)+5h=0\\\\h(h+5)=0\\\\\therefore h=0\\orh=-5`