For problems 1-10, express your answers in a Cartesian basis specified by the or

Question

For problems 1-10, express your answers in a Cartesian basis specified by the orthonormal basis elements x, y, and z. Define the following vectors: A = 3x - 6y + 1z B = -2x -1y + 9z Determine the magnitude of vector A. Determine the scalar product of vectors A and B, i.e determine A B. Determine the projection A onto the z-direction. Determine the cross product (or vector product) of A and B, i.e determine A Times B. Determine the angle between vectors A and B. Determine the vector sum of A and B, i.e. determine A + B. Determine the expression for a unit vector (i.e., a vector having a magnitude equal to 1) that points in the same direction as B. Determine the scalar product of vectors x and y, i.e determine x y. Determine the angle between vectors A and y. Determine the the expression for a unit vector (i.e., a vector having a magnitude equal to 1) that points in a direction that is perpendicular to both A and B.

Explanation / Answer

1.) A= sqrt(9+36+1)=6.78

2.)a · b = ax · bx + ay · by + az · bz = 3 · (-2) + (-6) · (-1) + 1 · 9 = -6 + 6 + 9 = 9

4.) = i (-54 + 1) - j (27 + 2) + k (-3 - 12) = {-53; -29; -15}

3.)a · b = ax · bx + ay · by + az · bz = 3 · 0 + (-6) · 0 + 1 · 1 = 0 - 0 + 1 = 1

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