If A= <16 ,-4 ,-1 >A=<16,−4,−1> and B= <2 ,-9 ,3 >B=<2,−9,3>, what is A*B -||A|| ||B||A⋅B−||A||||B||?

1 Answer
Faizan B.
Feb 6, 2016

65-sqrt(25662) ≈ -95.1965−√25662≈−95.19

Explanation:

Since A • B=x_1x_2+y_1y_2+z_1z_2A∙B=x1x2+y1y2+z1z2, the A • BA∙B term equals (16*2) + (-4*-9) + (-1*3)(16⋅2)+(−4⋅−9)+(−1⋅3), which is 65.

Since the magnitude of a vector is given by sqrt(x^2+y^2+z^2)√x2+y2+z2, the magnitude of A is sqrt(16^2+(-4)^2+(-1)^2√162+(−4)2+(−1)2, which equals sqrt(273)√273.

Likewise, the magnitude of B is sqrt(2^2+(-9)^2+(3)^2√22+(−9)2+(3)2, which equals sqrt(94)√94

Therefore, the equation A⋅B−||A||||B||A⋅B−||A||||B|| simplifies to 65-sqrt(273)*sqrt(94)65−√273⋅√94 which further simplifies to 65-sqrt(25662)65−√25662, which is approximately -95.19

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