Find two unit vectors that are perpendicular to both j + 4k and i − 2j + 3k.

Question

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Answer 1

Let v = J + 4k and w = i - 2j + 3k

The cross product, v x w, is perpendicular to both v and w

v x w is the "determinant" of the 3x3 matrix with first row i j k, second row 0 1 4, and third row 1 -2 3

v x w = 11i + 4j - k

ll v x w ll = magnitude of v x w = √[11² + 4² + (-1)²] = √138

Two unit vectors perpendicular to both v and w are (1 / llv x wll)(v x w) and (-1 / llv x wll)(v x w).