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midterm review

# midterm review - 1 The dot product is a while the cross...

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1. The dot product is a ________ while the cross product is a _________ 2. Two vectors whose dot product is 0 are ____________, two vectors whose cross product is 0 are __________ 3. Find the volume of the parallelepiped determined by i + 2 j – 3 k , 2 i j + 2 k , - i j +3 k 4. Find parametric equations for the line through the point (0,-1,2) that is parallel to the plane 2x - y + 3z = 4 and perpendicular to the line x = 2 + t, y = 1 – t, z = 3 +2t 5. Find the distance between the given parallel planes 4x + 8y – 10z = 6, 2x + 4y – 5z = 1 6. Find an equation for the plane that passes through the line of intersection of the planes x - 2z = 1 and y – z = 3 and is perpendicular to the plane x – y + 2z = 2 7. Are the lines defined by the following equations parallel, intersecting or skew? L1: x = t, y = 1+2t, z=2+3t L2: x=3-4s, y=2-3s, z=1+2s 8. A curve has the given vector equation: r (t) = <1, 2cos(t), sin(t)> a) Write parametric equations for the curve b) Sketch the curve 9. Two particles are traveling on different paths given by r 1 (t) = <t, t + 1, t 2 + 1> and r 2 (s) = <8s – 5, s + 3, 10s >

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midterm review - 1 The dot product is a while the cross...

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