27_new - DiscGQ06 gilbert (55035) This print-out should...

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DiscGQ06 – gilbert – (55035) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find an equation for the plane passing through the origin and parallel to the plane x + 4y − 2z = 1 . 1. 4x + 2y + 4z = 0 2. 4x − 2y − 4z + 1 = 0 3. 2x + y − 4z + 1 = 0 4. x + 4y − 2z = 0 correct 5. 2x − y + 4z = 0 6. x − 4y + 2z + 1 = 0 Explanation: The scalar equation for the plane through P (a, b, c) with normal vector n = Ai + Bj + Ck is A(x − a) + B(y − b) + C(z − c) = 0 . But P (a, b, c) = (0, 0, 0) if the plane passes through the origin, while n = i + 4j − 2k if the plane is parallel to x + 4y − 2z = 1 since parallel planes have the same normal vector. Consequently, the plane has equation x + 4y − 2z = 0 . 002 10.0 points Which of the following expressions are well-defined for all vectors a, b, c, and d? I (a · b) × (c · d) , II a · (b × c) , III a × (b × c) . 1. I and III only 2. III only 3. II only 4. I and II only 5. II and III only correct 6. I only 7. all of them 8. none of them
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27_new - DiscGQ06 gilbert (55035) This print-out should...

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