SecJEx1W01 - whose acceleration is a (t)= < 2...

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Murat Atmaca Winter 2001 Math 22 Exam#1 1. Consider P(1,2,3), Q(3,5,6), R(-2,0,2) and S(6,-1,4). Let a = -→ PQ , b = -→ QR and c = -→ RS . Find the followings; (a) | a | = (b) 3 a - 2 b = (c) The unit vector of c (d) comp a b = (e) The angle θ between the vectors a and c 2. Find the symmetric equation and parametric equation of the line containing the point P(6, 12,0) and perpendicular to the plane 9x+3y-6z=30. 3. Given a =2 i +1 j +x k and b= < x, - 3 , x > . Then If the vectors a and b are orthogonal each others, then find all values of x . 4. Given a =8 i +4 j -12 k and b = < x, - 3 , z > . If the vectors a and b are parallel each others, then find the values of x and z . 5. Find both the position function vector and the velocity function vector for a particle
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Unformatted text preview: whose acceleration is a (t)= &lt; 2 sin(2 t ) , 3 , t &gt; , if its initial velocity is v (0) =k and its initial position is r (0)= j . 6. Find an equation of the plane that passes through the points P(1,2,3) and contains the line x=3t , y=1+t , and z=2-t . 7. Convert the point (4, 4 ,4) from the cylindrical coordinates to the spherical coordinates. 8. Suppose that r(t) parameterized a space curve C so that r (1)=3 i + 1 3 k , v (1)=2 i-2 j + k and a (1)=-2 j +2 k . Find the following: (a) The speed at t=1 (b) T (1) = (c) B (1) = (d) The curvature at t=1 (e) a T at t=1...
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