In Exercises 1-8, find
(a) \(\mathbf{u} \cdot \mathbf{v}\),
(b) \(\mathbf{u} \cdot \mathbf{u}\),
(c) \(\|\mathbf{u}\|^{2}\),
(d) \((\mathbf{u} \cdot \mathbf{v}) \mathbf{v}\), and
(e) \(\mathbf{u} \cdot(\mathbf{2 v})\).
\(\mathbf{u}=\langle-4,8\rangle, \mathbf{v}=\langle 7,5\rangle\)
Text Transcription:
u dot v
u dot u
||u||^2
(u dot v) v
u dot(2 v)
u=langle-4,8 rangle, v=langle 7,5 rangle
Step 1 of 5) To evaluate the integrals in Equations (5), we picture the plate in the coordinate plane and sketch a strip of mass parallel to one of the coordinate axes. We then express the strip’s mass dm and the coordinates (x , y ) of the strip’s center of mass in terms of x or y. Finally, we integrate y dm, x dm, and dm between limits of integration determined by the plate’s location in the plane.
