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Unformatted text preview: homework 05 – KERR, KELSEY – Due: Feb 1 2008, 11:00 pm 1 Question 1, chap 3, sect 4. part 1 of 3 10 points Consider two vectors vector A and vector B shown on the following isometric diagram: A B x y z On this diagram, the coordinate axes x , y , and z are shown as blue lines with ticks, each tick denoting one unit of distance. The vectors vector A and vector B are shown as black lines with arrow; both vectors begin at the origin of the coor dinate system. The green dotted lines help locate the end points of vectors in 3D. For each vector, one dotted line is horizontal and projects onto the z components of the vector; the other dotted line is vertical and projects onto the green dot in the ( x, y ) plane, from which two more dotted line project onto the x and y components of the vector. Find the vertical component of vector A × vector B . Correct answer: 7 units 2 (tolerance ± 1 %). Explanation: See Eq. 2 in the next part. ( vector A × vector B ) z = bracketleftBig A x B y − A y B x bracketrightBig ˆ k = bracketleftBig (5 units) (3 units) − ( − 4 units) ( − 2 units) bracketrightBig ˆ k = 7 units 2 ˆ k . Question 2, chap 3, sect 4. part 2 of 3 10 points What is the magnitude of the vector prod uct of these two vectors? Correct answer: 11 . 7473 units 2 (tolerance ± 1 %). Explanation: Basic Concept: vector A × vector B = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı ˆ ˆ k A x A y A z B x B y B z vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle (1) = vextendsingle vextendsingle vextendsingle vextendsingle A y A z B y B z vextendsingle vextendsingle vextendsingle vextendsingle ˆ ı + vextendsingle vextendsingle vextendsingle vextendsingle A z A x B z B x vextendsingle vextendsingle vextendsingle vextendsingle ˆ + vextendsingle vextendsingle vextendsingle vextendsingle A x A y B x B y vextendsingle vextendsingle vextendsingle vextendsingle ˆ k = ( A y B z − A z B y )ˆ ı + ( A z B x − A x B z )ˆ + ( A x B y − A y B x ) ˆ k Let : A x = 5 units , A y = − 4 units , A z = − 1 units , B x = − 2 units , B y = 3 units , and B z = 2 units . Solution: Using Eq. 1, we have vector A × vector B = bracketleftBig A y B z − A z B y bracketrightBig ˆ ı + bracketleftBig A z B x − A x B z bracketrightBig ˆ + bracketleftBig A x B y − A y B x bracketrightBig ˆ k (2) = bracketleftBig ( − 4 units) (2 units) − ( − 1 units) (3 units) bracketrightBig ˆ ı + bracketleftBig ( − 1 units) ( − 2 units) − (5 units) (2 units) bracketrightBig ˆ + bracketleftBig (5 units) (3 units) − ( − 4 units) ( − 2 units) bracketrightBig ˆ k = ( − 5 units 2 )ˆ ı + ( − 8 units 2 )ˆ homework 05 – KERR, KELSEY – Due: Feb 1 2008, 11:00 pm 2 + (7 units 2 ) ˆ k bardbl vector A × vector B bardbl = braceleftBig ( − 5 units 2 ) 2 + ( − 8 units 2 ) 2 + (7 units 2 ) 2 bracerightBig 1 / 2 = 11 . 7473 units 2 ....
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 Spring '08
 Turner
 Cartesian Coordinate System, Dot Product, Work, Correct Answer, Ax Bz

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