if the vector 2i+3j+8k is perpendicular to the vector 4i-4j+ak then the value of a is

(2i+3J+8k). (4j-4i+ak) =0We find the dot product for perpendicular vectors which is equal to zero.On solving we get -8+12+8a=0Giving, a=-1/2

Hello Student

Let a = 2i + 3j + 8k and b = 4i - 4j + ak
As a and b are perpendicular to each other then their Dot product os Zero
=> a . b = 0
=> ( 2i + 3j + 8k ) . ( 4i - 4j + ak ) = 0
=> 2 × 4 + 3 × (-4) + 8 × a = 0
=> 8 - 12 + 8a = 0
=> – 4 + 8a = 0
=> 8a = 4
=> a = 1 / 2

I hope this answer will help you.