Question

For what value of x will the two vectors a vector is equals to 2 ICAP + 4 j cap - x k cap and b is equals to 4 ICAP - J cap + 4 k cap are perpendicular to each other

Answer 1

Answer: A.B=0

(2i +4j -x k). (4i -j +4k) =0

8 -4 -4x = 0

4=4x

x=1 Ans

Explanation:

A.B= ABcosФ

Perpendicular=Ф=90°

And cos90°=0

Answer 2

Answer:

x= 1

Explanation:

Given that

Vector A = 2 i + 4 j - x k

Vector B = 4 i - j + 4 k

As We know if dot product(A.B) of two vector are zero then we can say that vectors are perpendicular to each other.

We also know that

i x i = j x j = k x k =0

i.i=j.j=k.k=1

Vector A = 2 i + 4 j - x k

Vector B = 4 i - j + 4 k

A.B= 0 ( perpendicular to each other)

(2 i + 4 j - x k) . (4 i - j + 4 k) = 0

8 -4 - 4 x = 0

4 - 4 x

x= 1