Question

If the two vectors A=2i+3j+4k and B=i+2j-nk are perpendicular, then find the value of n.

Answer 1

Answer:

Explanation:

Here ,

A=2i+3j+4k and B=i+2j-nk

We know that,

A.B= ABcosθ

Since the two vectors are perpendicular to each other ,So θ=90°

Hence A.B=ABcos90°

A.B = 0 (cos90°= 0)

So,

(2i+3j+4k) .(i+2j-nk )=0

2+6-4n=0 ( because i.j=0 & i.i=1)

8-4n=0

n= 2

Answer 2

Given:

First vector A = 2i+3j+4k

Second vector B = i+2j-nk

To find:

The value of n.

Solution:

If the given vectors are perpendicular to each other, then their dot product will be zero. Thus, if we find the dot products of the given vectors, their dot product will also be zero since these vectors are perpendicular to each other.

(2i+3j+4k) · (i+2j-nk) = 0

= 2 + 6 - 4n = 0

On further solving, we get:

4n = 8

n = 2

Thus, the value of n is 2.