Which of the following vectors is perpendicular to 𝑎=(1,2,3) a = ( 1 , 2 , 3 ) and 𝑏=(1,−1,2) b = ( 1 , − 1 , 2 ) ?

Question

which of the following is perpendicualr to said vector

Answer 1

Bradford gives one process but has a typo in his first inner product (it should be 1 as the middle number). Find vectors whose inner product with each of a and b is 0. Another is to do the cross-product and see which is a multiple of the cross-product

i j k

1 2 3

1 -1 2

has determinant 7i + j - 3k

Thus, the solution will be multiples of (7, 1, -3), in particular, the obvious (7, 1, -3)

Answer 2

Need to find the vector or vectors that both the dot product of a and the dot product of b are zero.

a•(7,-1,-3) = 7+2-9 = 0

b•(7,1,-3) = 7-1-6 = 0

etc