Mathematics

Problem

Answer the following questions about scalar components of vectors: a. (a) Define the scalar component (projection) of a vector

\vec a

on another non-zero vector

\vec b

and explain how its sign is determined. b. (b) Given

\vec p = -3\mathbf{i} + 4\mathbf{j}

and

\vec q = 5\mathbf{i} + 12\mathbf{j}

, find the scalar component of

\vec p

\vec q

and of

\vec q

\vec p

. Comment on the difference between the two numerical results. c. (c) Justify whether the scalar component of a vector on itself can ever be negative.

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