SecFEx1W01 - M.Thomas Winter 2001 Math 22 Exam#1 1. Given...

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Unformatted text preview: M.Thomas Winter 2001 Math 22 Exam#1 1. Given the vectors a =< 4, −1, 2 > and b =< −1, 3, 5 > find (a) the unit vector in the direction of b − a (b) the scalar projection of a onto b (c) the vector projection of b onto a 2. Find the distance between the planes 4x + 3y − z = 2 and 8x + 6y − 2z = −1. 3. Find the angle between the planes 2x + 4y − z = 1 and 2x − y + z = −1 to the nearest degree. 4. Determine if the lines L1 : x = 5 + 3t, y = −1 + 2t, z = 5 − t L2 : x = 18 + 3s, y = 3 − s, z = −8 − 2s are parallel, skew, or intersecting. If they intersect, list the point of intersection. 5. Find parametric equations for the line through the point (1, −2, 3) that is parallel to the plane 3x − y + 5z = 3 and perpendicular to the line x = 2 + t, y = −2t, z = 4 − t. 6. Identify the surface whose equation in spherical coordinates is ρ2 cos(2φ) = 3. 7. Determine the domain of the curve r(t) = t3 i + ln(16 − t2 )j − (te−t + e−t )k . Then determine if the curve is smooth over its domain. 8. Find the radius of the osculating circle to the curve r(t) =< t2 , 1 − t, 2t > at the point (0, 1, 0). 9. Find the length of the arc along the curve r(t) = sin ti − cos tj + 4tk between t = 2 and t = 3. 10. Find the tangential and normal components of the acceleration vector given that the position vector function is r(t) =< t2 , 1 − 2t, e2t >. ...
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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