What are the values of a and b if vectors `a hati+b hatj = hatn and (hati+hatj)` are perpendicular to each other ?

What is the value of x so that the vector 6hati+2hatj-3hatk and hati-4hatj+xhatk are perpendicular to each other.

Show that vectors vecA= 3hati+ hatj+ hatk and vecB= hati+ 2hatj- 5hatk are perpendicular to each other.

Prove that the vectors vec(A) = hati +2 hatj +3hatk and vec(B) = 2hati - hatj are perpendicular to each other.

What is the value of a, if two vectors vec P =hati+12 hatj+hatk and vec Q =2hati-ahatj+4hatk are perpendicular to each other ?

For what value of lambda , the vectors veca=3hati+4hatj and vecb=8hati+lambdahatj are perpendicular to each other.

For what values of a and b , will the vectors 2hati-3hatj-hatk and ahati+bhatj-2hatk be parallel to each other ?

for what value of lambda, the vectors veca=3hati-hatj+4hatk , b= lambdahati+3hatj+3hatk are perpendicular to each other

For what value of a are the vectors vec(A) = a hati - 2hatj +hatk and vec(B) = 2a hati +a hat j - 4hatk perpendicular to each other ?

For what value of lamda are the vectors veca=2hati+lamda hatj+hatk and vecb=hati-2hatj+3hatk perpendicular to each other ?

For what value of x , will the two vector A= 2hati + 2hatj -x hatk and B =2 hati - hatj - 3hatk are perpendicular to each other ?