Question

Find the cross product (7,9,6) x (-4,1,5) is the resulting vector perpendicular to the given vectors?

Answer 1

Given:  <7,9,6> x <-4,1,5>

To find: cross product?

Solution:

• As we know that cross product of 2 vectors is given by:

          <u1 u2 u3> x <v1 v2 v3> = < u2v3 - v2u3 , u1v3 - u3v1 , u1v2 - u2v1 >

• So using this, we get:

          <7,9,6> x <-4,1,5> = <45-6 , 35-(-24) , 7-(-36)) >

                                        = < 39 , -59 , 43 >

• Verifying by making dot product, we get:

          <u1 u2 u3> . <v1 v2 v3> = u1v1 + u2v2 + u3v3

• Putting values in formula. we get:

          < -4 , 1 , 5 > . < 39 , -59 , 43 > = -156 - 59 + 215

                                                           = 0

          Similarly, <7,9,6> . < 39 , -59 , 43 > = 0

• As both dot products are  =0  so the vector is perpendicular to the other 2 vectors also.

Answer:

                    Both dot products are  =0  so the vector is perpendicular to the other 2 vectors also.