Calculating Vector Projection Using Trigonometry

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SUMMARY

The discussion focuses on calculating vector projection using trigonometry with two vectors: avector = 3.5i + 4.5j and bvector = 2.0i + 5.0j. The results for the cross product (a) are 8.5k, the dot product (b) is 29.5, and the dot product of the sum of the vectors (c) is 58.5. However, the calculation for the component of avector along the direction of bvector (d) is incorrect; the user initially calculated it as 16.2 degrees using the cosine formula, which was later clarified to require a different approach for accurate projection.

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Two vectors are given by avector = 3.5i + 4.5j and bvector = 2.0i + 5.0j. Find the following:

(a) avector x bvector

(b) avector ·bvector

(c) (avector + bvector ) · bvector

(d) the component of avector along the direction of bvector
these are the answers i got

a)8.5k
b) 29.5
c) 58.5
d)16.2

i know that a through c are correct but d is incorrect, i calculated d by

cos-1 (29.5/(5.7*5.39) = 16.2

the 5.7 came from sqrt(3.5²+4.5²)
5.39 came from sqrt(2²+5²)

thanks in advance
 
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OK, so the angle between the vectors is 16 degrees. What did you do to calculate the projection of A on B?
 

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