Find the scalar projection and vector projection of b = 3, 1, 2 onto a = −4, 1, 3 .
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Zhumagali S.
EXAMPLE 6 Find the scalar projection and vector projection of b = (3, 1, 1) onto a = (-4, 2, 3). SOLUTION Since |a| = √((-4)² + 2² + 3²) = √29, the scalar projection of b onto a is compₐb = (a · b) / |a| = ((-4)(3) + 2(1) + 3(1)) / √29 = -(7√29) / 29 The vector projection is this scalar projection times the unit vector in the direction of a, below. projₐb
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Find the scalar and vector projections of b onto a. a = (4, 7, -4) b = (4, -1, 1) scalar projection of b onto a vector projection of b onto a
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