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Homework 5 Solutions

Homework 5 Solutions - HOMEWORK 05 Solutions(1 Suggested...

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HOMEWORK 05 Solutions (1) Suggested Problems (2) Suggested Problems (3) (a) Since v 1 is parallel to the xz plane, its j component will be zero. Also, the ratio of the k component to the i component will be f x ( P 0 ) in order to have this as its slope. v 1 = i + f x ( P 0 ) k satisfies these conditions. For v 2 , the i component will be zero for it to be parallel to the yz plane. The ratio of the k component to the j component will be f y ( P 0 ). Hence, we can use v 2 = j + f y ( P 0 ) k . (b) To find n we take the cross product of v 1 and v 2 : n = v 1 × v 2 = i j k 1 0 f x ( P 0 ) 0 1 f y ( P 0 ) = f x ( P 0 ) i f y ( P 0 ) j + k (c) From our vector n and point P 0 ( x 0 , y 0 , z 0 ), we can write the equation of our plane as: f x ( P 0 )( x x 0 ) f y ( P 0 )( y y 0 )+( z z 0 ) = 0. In standard form, this is: f x ( P 0 ) x + f y ( P 0 ) y z = f x ( P 0 ) x 0 + f y ( P 0 ) y 0 z 0 . (d) First, we determine where S intersects the x , y , and z axes. To find the point P 1 where S intersects the z axis, set x and y equal to zero in our equation: z = 4 P 1 (0 , 0 , 4). Similarly, to find where S inter- sects the x axis, set y and z
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