Calculating Vector Projection Using Trigonometry

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The discussion revolves around calculating vector projections using trigonometry with two vectors: avector = 3.5i + 4.5j and bvector = 2.0i + 5.0j. The calculations provided include the cross product (8.5k), dot product (29.5), and the result of adding the vectors and dotting with bvector (58.5). However, the component of avector along bvector was initially calculated incorrectly as 16.2 degrees. The correct method for calculating the projection of avector on bvector was questioned, indicating a need for clarification on the projection formula.
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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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