Question

for what value of a are the vectors A =ai^-2j^+k^ and B =2ai^+aj^-4k^ perpendicular to each other?

Answer 1

Hope this will help you

Answer 2

Given,

Vector A=ai^-2j^+k^,

vector B=2ai^+aj^-4k^

To Find,

Value of a.

Solution,

To prove perpendicular dot product of vector A and vector B should be zero.

So, A. B=0

  ⇒(ai^-2j^+k^) .(2ai^+aj^-4k^)=0

  ⇒2a²-2a-4=0

  ⇒a²-a-2=0

  ⇒a²-2a+a-2=0

  ⇒a(a-2)+1(a-2)=0

  ⇒(a-2)(a+1)=0

   ⇒a=2 or -1

Hence, value of a will be 2 or -1 so that two vectors will be perpendicular to each other.