Answer :
Answer:
The vectors are perpendicular for:
1) h = 0
2) h = -5
Step-by-step explanation:
For two vectors to be perpendicular the dot product of the 2 vectors should be zero
The given vectors are
[tex]\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}[/tex]
The dot product is calculated as
[tex]\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[/tex]