HW09-solutions

Keywords determinant cross product vector product

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Unformatted text preview: he plane. But 4 Here − − → P Q = −3, 4, 0 , − → P R = −3, 0, 2 . =4 2 −3 3 −3 −4 3 2 −3 2 a · ( b × c) = −1 3 −3 + 3 −3 2 −3 −4 32 23 . geyer (dag2798) – HW09 – rusin – (55735) 4 Consequently, keywords: line, parametric equations, direction vector, point on line, intercept, coordinate plane volume = 11 . keywords: determinant, cross product, vector product, scalar triple product, parallelopiped, volume, 007 008 10.0 points Find parametric equations for the line passing through the points P (4, 1, 2) and Q(5, 5, 5). 10.0 points A line ℓ passes through the point P (1, 4, 4) and is parallel to the vector 2, 3, 4 . At what point Q does ℓ intersect the xy plane? 1. x = 4 + t, correct y = 1 + 4t, z = 2 + 3t 2. x = 4 − t, y = 1 + 4t, z = 2 − 3t 3. x = 1 + 4t, y = 4 − t, z = 3 + 2t 1. Q(1, −1, 0) 4. x = 1 + 4t, y = 4 + t, z = 3 + 2t 2. Q(0, −1, 7) 5. x = 1 − 4t, y = 4 + t, z = 3 − 2t 3. Q(−1, 1, 0) correct 6. x = 4 + t, y = 1 − 4t, z = 2 + 3t 4. Q(0, 7, 3) Explanation: A line passing through a point P (a, b, c) and having direction vector v is given parametrically by 5. Q(0, 3, 1) 6. Q(3, 7, 0) Explanation: Since the xy -plane is given by z = 0, we have to find an equation for ℓ and then set z = 0. Now a line passing through a point P (a, b, c) and ha...
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This note was uploaded on 05/12/2013 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.

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