# Chapter 8 - Polar Coordinates; Vectors - Section 8.4 Vectors - 8.4 Assess Your Understanding - Page 627: 42

$13i-21j$

#### Work Step by Step

Let us consider two vectors $v=pi+qj$ and $w=xi+yj$; then we have: $v \pm w=(p \pm x)i+(q \pm y)j$ The magnitude of any vector (let us say $v$) can be determined using the formula $||v||=\sqrt{p^2+q^2+r^2}$ Therefore, $3v -2w= 3(3i-5j) -2(-2i+3j) \\ = 9i-15j +4i -6j \\ = 13i-21j$

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