four vectors are listed below. A=4i+10j, B=2i-5j, C=-6i+15j, D=15i-6j. which pair of the vectors is orthogonal?
A.A and B
B.B and C
C.A and D
D.C and D
B.B and C
In order to determine if two vectors are orthogonal, we need to calculate their dot product and check if it equals zero.
Let's calculate the dot products for each pair of vectors:
A and B: A·B = (4 * 2) + (10 * -5) = 8 - 50 = -42
B and C: B·C = (2 * -6) + (-5 * 15) = -12 - 75 = -87
A and D: A·D = (4 * 15) + (10 * -6) = 60 - 60 = 0
C and D: C·D = (-6 * 15) + (15 * -6) = -90 - 90 = -180
From the calculations, we can see that the only pair of vectors with a dot product of zero, thus making them orthogonal, is A and D.
Therefore, the correct answer is C. A and D