MATH1151 week10c2 - Week 10 Tuesday 10-11 Class Time...

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Time allowed: 20 minutes. 1. (2 marks) Find the equation of the plane x +3 y 2 z = 12 in parametric and point-normal form. 2. (2 marks) Find the points of intersection (if any) of the line ˜ x = ± 9 3 ² + λ ± 4 3 ² for λ R and the circle with radius 5 and centre ± 7 9 ² . 3. (2 marks) Find the volume of the parallelepiped spanned by 1 2 0 , 1 2 1 and 3 1 2 . 4. (4 marks) Suppose that A = 50 0 0 1 21 4 a 37 102 20 30 0 0 1 40 0 2 1 108 200 1 1 2 . (a) Without doing any calculations, state a value of a for which A is not invertible. (b) If det( A )= 84, determine the value of a . Week 10 Tuesday 10-11 Class
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1. x +3 y 2 z =12 (a) ˜ a = 12 0 0 is a point on the plane, and a normal to the plane is ˜ n = 1 3 2 (coefficients of x, y, z ). The Point-Normal form of the plane is ( ˜ x ˜ a ) · ˜ n = ˜ 0: x y z 12 0 0 · 1 3 2
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MATH1151 week10c2 - Week 10 Tuesday 10-11 Class Time...

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