Trig Question?

Question

Please explain to me how to do this problem:


Determine m such that the two vectors are orthogonal(perpendicular).

(1) 4mi + j , 9mi-25j


(2) 5mi + 3j , 2i + 7j



Thanks

Answer 1

Perpendicular vectors have a dot product equal to zero. Two vectors and (or a1i + a2j and b1i + b2j) have the dot product a1*b1 + a2*b2. So in the case of 1), the dot product is 4m*9m + 1*-25 = 36m^2 - 25. Set it equal to 0 and solve; you should get two answers, and they are both valid. For 2), the dot product is 5m*2 + 3*7 = 10m + 21. Again, set it equal to 0 and solve.

Answer 2

If the dot product of two vectors is zero, then the vectors are orthogonal.

4mi + 1j dot 9mi -25j
4m*9m + 1*-25 =0
36m^2 -25=0
36m^2=25
m=(plus or minus) 5/6
-----------------------------
5mi + 3j , 2i + 7j
5m*2 + 3*7=0
10m+21=0
m=-2.1