(a) In unit-vector notation, what is the sum of a Overscript right-arrow EndScri

Question

(a) In unit-vector notation, what is the sum of a Overscript right-arrow EndScripts equals left-parenthesis 4.6 m right-parenthesis i Overscript EndScripts plus left-parenthesis 1.1 m right-parenthesis j Overscript EndScripts and b Overscript right-arrow EndScripts equals left-parenthesis negative 12.0 m right-parenthesis i Overscript EndScripts plus left-parenthesis 6.8 m right-parenthesis j Overscript EndScripts. What are (b) the magnitude and (c) the direction of a Overscript right-arrow EndScripts plus b Overscript right-arrow EndScripts (relative to i Overscript EndScripts)?

Explanation / Answer

(a) Vector a = 4.6 i - 1.1 j
  Vector b = -12 i + 6.8 j
(b) Now vector a + b = -7.4 i + 5.7 j
  magnitude = (7.42 + 5.72)1/2 = 9.34 m
  direction
angle = tan-1(-5.7/7.4) = -37.61

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