samplx1s10

samplx1s10 - L that goes through the point r (0) . 5. (15...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 23 Sample First Exam was: February, 2003 NAME : Section (Last, First) 1. (15 points ) If ± U, ± V and ± W are the vectors ± U = ± i - 3 ± j + ± k, ± V = 2 ± i - ± j + 3 ± k and ± W = - ± i + 2 ± j - ± k, where ± i, ± j and ± k are the unit vectors in the direction of the coordinate axes, find the following. (a) the dot product of ± U and ± V (b) the scalar projection of ± V onto ± W (= component of ± V in the direction of ± W ) (c) the vector projection of ± V onto ± W 2. (10 points ) Find the center and radius of the sphere with equation x 2 - 6 x + y 2 + 2 y + z 2 = 3 . 3. (15 points ) (a) Find a vector perpendicular to the plane through (3 , 0 , - 1) , (2 , 1 , - 5) and (1 , 2 , - 4) . (b) give an equation for the plane in part (a). 4. Let L be the line given by the vector equation ± r ( t ) = < - 2 , 4 , 1 > + t < 3 , 2 , 4 > . (a) (5 points ) Find the point P that is on both the line L and the xz -plane (the one with equation y = 0). (b) (5 points ) Find an equation of the plane perpendicular to the line
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L that goes through the point r (0) . 5. (15 points ) Find an equation for the tangent line to the curve- r ( t ) = t 3 i-2 t j-2 t 2 k at the point P (-1 , 2 ,-2) . 6. (15 points ) (a) If- r ( t ) = &lt; t, 3 cos t, 3 sin t &gt;, nd the unit tangent vector T ( t ). (b) Find T and N at the point (0 , 3 , 0) . 7. (20 points ) The position function for the motion of a particle is given by- r ( t ) = ( 2 3 t 3 ) i + 2 t j + t 2 k = &lt; 2 3 t 3 , 2 t, t 2 &gt; . (a) Find the acceleration vector. (b) Find the tangential component a T of acceleration. (c) What is the normal component when t = 0? (= a N (0)) (d) How fast is the particle speeding up at time t = 1?...
View Full Document

Ask a homework question - tutors are online