Find the quantity if v 5i 7j and w 4i 2j 4v 5w 4v 5w

Find the quantity if v = 5i - 7j and w = -4i + 2j. 4v + 5w 4v + 5w = ____ (Simplify your answer. Type your answer in the form ai + bj.)

Solution

multiplying by a scalar is just same as increasing the magnitude without changing the direction so simple multiplication of the scalar with all of the component is enough

v = 5i -7j

4V = 20i - 28j

w = -4i + 2j

5w = -20i + 10j

4v + 5w = (20i -20i ) + (-28j + 10j)

4v + 5w = 0i -18j

a = 0

b = -18