1302_HA7

1302_HA7 - + = which is perpendicular to b a n n and . 8....

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EGR 1302 Homework Assignment #7 1. Obtain the scalar products of the pairs of vectors: ) 10 , 9 , 8 ( ) 3 , 2 , 1 ( and ) 2 , 1 , 3 ( ) 1 , 2 , 2 ( - - and ) 1 , 1 , 4 ( ) 3 , 2 , 3 ( - - and 2. Evaluate b a n n if k j i a ˆ ˆ ˆ 2 + - = and k j i b ˆ 2 ˆ 2 ˆ 3 - + = . 3. From #2, Find ) ( ) ( a b b a n n n n - - and ) ( ) ( b a b a n n n n + - . 4. Find the angles, in the range 180 to 0 , between the vectors given in #1. 5. For ) 1 , 2 , 2 ( : - - A , ) 1 , 1 , 0 ( : B , ) 3 , 2 , 1 ( : C , find the angles in the triangle ABC . 6. The component of a vector in the direction of another vector is given by a a F n n n / . Find the components of ) 9 , 15 , 8 ( : F n in the direction of the three vectors ) 6 , 3 , 2 ( = a n , ) 4 , 3 , 0 ( = b n , and ) 1 , 2 , 2 ( = c n . Then express F n in the form c b a F n n n n ν μ λ + + = , where , , are constants. 7. Show that the vectors k j i a ˆ 4 ˆ 3 ˆ + + = and k j i b ˆ 4 ˆ 6 ˆ 2 - + - = are perpendicular. Find any vector k c j c i c c ˆ ˆ ˆ 3 2 1 +
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Unformatted text preview: + = which is perpendicular to b a n n and . 8. Determine the numbers , , which ensure that the vectors ) 3 , 2 , (-= a n , ) 2 , 2 , 1 (-= b n and ) 3 , 1 , 2 (-= c n are mutually perpendicular. 9. Find the lengths, and the direction cosines n m l , , of the following vectors; ) 6 , 3 , 2 ( = a n ) 4 , 3 , ( = b n ) 1 , 2 , 2 ( = c n 10. The angles made by vector a n and the positive directions of the axes z x O O , are 45 and 30 respectively. Find the angle that a n may make with y O ....
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