Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors B=(−3,0,1),C=(−1,−1,2) Dot product of two vectors multiplied by constants Calculate 2B―⋅3C―. Express your answer numerically. 2B―⋅3C―=

Question

Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors B=(−3,0,1),C=(−1,−1,2)  Dot product of two vectors multiplied by constants Calculate 2B―⋅3C―. Express your answer numerically. 2B―⋅3C―=

vicki331g8 · Accepted Answer

Dot product of two vectors multiplied by constants:  2B―⋅3C―=2(−3,0,1)⋅3(−1,−1,2)  ∴2B―⋅3C―=(−6,0,2)⋅(−3,−3,6)  ∴2B―⋅3C―=(−6×(−3))+(0×(−3))+(2×6)  ∴2B―⋅3C―=18+0+12  ∴2B―⋅3C―=30

Papilys3q · Accepted Answer

Is there a more shortly solution?

nick1337 · Accepted Answer

Here: The dot product of vectors 2B―⋅3C― is, Here, p and q are constans, Cx,Cy,Cz are the x,y,z components of vector C―, Substitute 2 for p, 3 for q, -1 for Cx, -1 for C_xCy, 2 for Cz, -3 for Bx, 1 for Bz. The dot product of the vectors is, 2B―⋅3C―=30