If #A= <2 ,-3 ,9 ># and #B= <0 , 3, 7 >#, what is #A*B -||A|| ||B||#?
1 Answer
# bb ul A * bb ul B - || bb ul A || \ || bb ul B || = 54 - sqrt(94)sqrt(58) #
Explanation:
We have:
# bb ul A = << 2, -3, 9 >># and# bb ul B = << 0, 3, 7 >>#
And so we compute the Scalar (or dot product):
# bb ul A * bb ul B= << 2, -3, 9 >> * << 0, 3, 7 >>#
# \ \ \ \ \ \ \ \ \ = (2)(0) + (-3)(3) + (9)(7) #
# \ \ \ \ \ \ \ \ \ = 0 - 9 + 63 #
# \ \ \ \ \ \ \ \ \ = 54 #
And we compute the vector norms (or magnitudes):
# || bb ul A || = || << 2, -3, 9 >> || #
# \ \ \ \ \ \ \ = sqrt( << 2, -3, 9 >> * << 2, -3, 9 >> ) #
# \ \ \ \ \ \ \ = sqrt( (2)^2+ (-3)^2 + (9)^2 ) #
# \ \ \ \ \ \ \ = sqrt( 4 + 9 + 81) #
# \ \ \ \ \ \ \ = sqrt( 94 ) #
Similarly,
# || bb ul B || = || << 0, 3, 7 >> || #
# \ \ \ \ \ \ \ = sqrt( << 0, 3, 7 >> * << 0, 3, 7 >> ) #
# \ \ \ \ \ \ \ = sqrt( (0)^2+ (3)^2 + (7)^2 ) #
# \ \ \ \ \ \ \ = sqrt( 0+9+49) #
# \ \ \ \ \ \ \ = sqrt( 58 ) #
So that:
# bb ul A * bb ul B - || bb ul A || \ || bb ul B || = 54 - sqrt(94)sqrt(58) #
