Precalculus<br />Test 2 Study Guide<br />3657600149860uu1714500149860Magnitude<br />354330085725Resultant<br />19431002095...
PC Test 2 study guide 2011
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PC Test 2 study guide 2011

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PC Test 2 study guide 2011

  1. 1. Precalculus<br />Test 2 Study Guide<br />3657600149860uu1714500149860Magnitude<br />354330085725Resultant<br />194310020955vvScalar<br />Vector<br />1.Find the magnitude and direction of:<br />a) 2vb) v+uc) -v+2ud) 12v-2u<br />2.Find the magnitude of the horizontal and vertical components of v and u.<br />3.a=2, 3, -1 and b=-7,1,-3<br />Write the ordered triple that represents each expression. Find the magnitude of the resultant vector.<br />a) a+bb) -a+2bc) 12a-bd) -b+4a <br />e) 3a+b+2bf) -13b<br />4.Write the vector as the sum of unit vectors. Find the magnitude of each vector.<br />a) 2,4b) -3,5c) -1,3,-2d) 12,3,-8 <br />5.Write the ordered pair or triple that represents YZ.<br />a) Y-2,5, Z2, 8b) Y-1,-5, Z3,7c) Y-4, 12, Z0, -3 <br />d) Y0,6,3, Z1,4,-3 e) Y-2,4,7, Z-3,5,2 <br />6.Find the inner (dot) product of each set of vectors. Are the vectors perpendicular?<br />a) 4,8∙6,-3 b) -6,7,5∙4,9,-3 c) -7,1,0∙4,0,-2<br />7.Find the cross product of each set of vectors. Verify that the resulting vector is perpendicular to the given vectors.<br />a) 4,8,2×6,-3,-1b) 5,-2,5×-1,0,-3c) -2,3,0×5,2,0 <br />8.Prove that for any vector a, a×-a=0<br />9.Use the definition of cross products to prove that for any vectors a, b, c, a×b+c=a×b+a+c<br />10.Graph the following points on the Polar plane.<br />a) 2, 180°b) -1, 3π4c) 3, -45°d) -2,-π6<br />11.Convert the polar coordinates into rectangular.<br />a) 2, 180°b) -1, 3π4c) 3, -45°d) -2,-π6<br />12.Convert the rectangular coordinates into polar.<br />a) -3,4b) (-5,-12)c) 3,-1d) 22,-22<br />13.Solve the equation for x and y. <br />a) 2x+y+xi+yi=5+4i<br />b) 2x-5yi=12+15i<br />c) 1+x+yi=y+3xi<br />14.Write the complex number in polar form.<br />a) -2+4ib) -42c) -1-3id) 6-8i<br />15.Write the complex number in rectangular form.<br />a) 2cos5π4+isin5π4b) cos-π6+isin-π6c) 2.5cos1+isin1<br />16. r represents the ____________ of the complex number.<br />

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