Question

Use the vectors shown to sketch 2u + v. (Assume that each point lies on the grid lines and that each grid line is spaced one unit apart.)

Answer 1

To sketch 2u + v, draw vector u to scale, replicate it to create 2u, then add vector v at the end of 2u; the tip of v marks the end of 2u + v.

Step-by-step explanation:

To sketch the vector 2u + v, begin by drawing vector u to scale. You might, for instance, represent 1 unit of distance as a line segment of 2 cm. Once u is drawn, duplicate it so that 2u stands for twice the length of u. Then, draw vector v starting at the head of 2u, following the direction and magnitude indicated by your scale. The endpoint of v represents the head of the vector 2u + v.

When dealing with vectors in two dimensions, you can use unit vectors i and j to denote directions on the x and y axes, respectively. These unit vectors help simplify the expression of a vector by indicating direction without concerning magnitude.