Consider the points A(1,5,4), B(3,1,2) D(3,k,2) with AD perpendicular to AB. What is AB, and what is AD with answer in terms of k

Question

vectors are involved dont know what to do.

Answer 1

The vector from A to B denoted by AB is given by 

 

AB = B - A = (3,1,2) - (1,5,4) = (2,-4,-2) 

 

Similarly 

 

AD = D - A = (3,k,2) - (1,5,4) = (2,k-5,-2) 

 

If AD is perpendicular to AB then their dot product is 0 so 

 

AB·AD = 2*2 -4*(k-5) + (-2)*(-2) = 4 -4*k + 20 + 4 = -4*k + 28 = 0

-4*k = -28

k = 7