Two points P(3, -7) and Q(-2, 5) are given.
(a) Calculate the components of the vector PQ
(b) Calculate the magnitude and direction of PQ
(c) Is PQ equivalent to the vector between the points R(-2, -4) and S(-7, 8)?
Solve
Show that for vectors u, v and w \[ \begin{align} (u + v) + w &= u + (v + w) \end{align} \ \] and \[ \begin{align} \parallel cv \parallel &= |c| \parallel v \parallel \end{align} \ \]
Solve
Two vectors \( v = \langle 1, 3 \rangle \) and \( w = \langle 2, 2 \rangle \) are given.
(a) What angle does v make with the x-axis?
(b) Find a vector u such that u + v = -w
Solve
Two vectors \( v = \langle -2, 5 \rangle \) and \( w = \langle 3, 4 \rangle \) are given. Find
(a) 1/3 w
(b) v + 2w
(c) w - v
Solve
Two vectors \( u = \langle 2, 1 \rangle \) and \( w = \langle 0, 4 \rangle \) are given.
Find a vector v such that u + v = 2w
Solve