1302_HA8

# 1302_HA8 - k j i a ˆ 6 ˆ 3 ˆ 2 = k j i b ˆ 3 ˆ 2 ˆ 6...

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EGR 1302 Homework Assignment #8 1. Find any two points on the line of intersection of the planes 1 = + + z y x and 4 2 2 = - + z y x . Then obtain the equation of the line in both vector parametric and cartesian form. 2. Given vectors ) 2 , 2 , 1 ( = a y , ) 1 , 1 , 3 ( = b y and ) 1 , 3 , 2 ( - = c y , Find b a y y × a b y y × a c y y × c a b y y y × ) ( b c a y y y × × 3. Using the Cross Product, find the Direction Ratios of the line of intersection of the planes 1 = + + z y x and 4 2 2 = - + z y x . Compare your result to your answer in Problem #1. 4. Show that k j i a ˆ 6 ˆ 3 ˆ 2 + + = and k j i b ˆ 3 ˆ 2 ˆ 6 - + = are perpendicular. Find any vector k c j c i c c ˆ ˆ ˆ 3 2 1 + + = which is perpendicular to both b a y y and such that ] , , [ c b a y y y is a right- handed set. 5. Find the Volume of a parallelepiped whose sides are defined by vectors
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Unformatted text preview: k j i a ˆ 6 ˆ 3 ˆ 2 + + = , k j i b ˆ 3 ˆ 2 ˆ 6-+ = and k i c ˆ 4 ˆ 4 + = . 6. A Force ) , , 2 ( = F y acts at point ) 3 , 2 , 1 ( : P . Find the moment vector M y this force produces about the Origin. 7. A Force F y of magnitude 3 Newtons acts at a point ) 2 , 1 , 1 ( :-P in the direction of k j i ˆ 2 ˆ 2 ˆ--. Find the moment about the origin, O M y . 8. Find the magnitude of the moment the Force F y (in Problem #7) creates about an axis defined by the position vector k i r ˆ 4 ˆ 4 + = ....
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