Math Homework Help Vectors Grade 12?

I'm studying for my math test but i can't seem to get/understand these two questions

1)The angle between the vectors A and B is 120 degrees. The magnitude of A is 2 and the magnitude of B is 4. Determine the scalar projection of 3A+4B on B

2)The Vector R is twice as long as the vector S. The angle between the vectors is 110 degrees.The vector projection of S on R is (2, -1, 7). Determine R

please show steps/work

1 Answer

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  • alex
    Lv 7
    7 months ago
    Favorite Answer

    1/

    the scalar projection of 3A on B = 3|A|cos120 = 3(2)(-1/2) = -3

    hence the scalar projection of 3A+4B on B = -3+4(4)=13

    2/

    Hint:

    The Vector R is twice as long as the vector S ---> |R| = 2|S|

    The vector projection of S on R is (2, -1, 7)

    ---> (S.R)R / |R|^2 = <2 , -1 , 7>

    and

    S.R = |S||R}cos110

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