V = 180i + 450j W= 3i +2j?

Question

Need to find v.w describe answer in practical term.

Answer 1

I expected real and imaginary terms

what is 180i ?

j450 is an imaginary term

Whatever just use the R>P function on a calculator
(Real to Polar)

Answer 2

You are asking for the dot product of two vectors. A dot product result is just a projection of one vector onto another.

The most common dot product is when finding the scalar x or y component of a vector V. The projection of V onto the X axis is just x = V cos(theta) where theta is the angle between V and the X axis. In i,j product format, we could write it as x = [180i + 450j]*i = 180i^2 = 180 in your case. Similarly, the x projection of W would be x = 3.

In your case Z = V*W = [180i + 450j]*[3i + 2j] = 3*180*i^2 + 2*450*j^2 = 540 + 900 = 1440. The two cross terms we'd normally find when multiplying this kind of terms become zero because i*j and j*i = 0. This results because the projection of orthogonal axes (like i and j) is zero; that's one of the definitions of orthogonality in fact.

Z is a scalar. In fact, all dot products result in scalars. Such is the nature of dot products. [Most, if not all, cross products on the other hand end up as vectors...go figure.]

In practical terms, suppose V is a force vector and W is a distance vector. Then the work performed is WE = V*W from the usual work function equation. Then the dot product gives us the amount of work done by the force vector moving along the W vector.

Answer 3

V.W=(180)(3) + (450)(2)= 540+900= 1440. If V is force and W is displacement then V.W is the work done. Any other formula with the dot product definition applies as a practical app.

Answer 4

v.w=(180X3)+(450X2)
=540i+900j.