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Answer: b
Explanation: Projection of A on B = (A . B)/|B|. Thus the answer is 40/6.4= 6.25.
To find the projection of vector A onto vector B, we use the formula:
[
text{proj}_B A = frac{A cdot B}{B cdot B} B
]
First, we need to find the dot products (A cdot B) and (B cdot B).
Given:
– (A = 10j + 3k)
– (B = 4j + 5k)
Calculating (A cdot B):
[
A cdot B = (0)(4) + (10)(5) + (3)(0) = 0 + 50 + 0 = 50
]
Calculating (B cdot B):
[
B cdot B = (0)(0) + (4)(4) + (5)(5) = 0 + 16 + 25 = 41
]
Now substituting into the projection formula:
[
text{proj}_B A = frac{50}{41} B
]
Now substituting (B):
[
text{proj}_B A = frac{50}{41} (4j + 5k) = frac{200}{41} j + frac{250}{41} k
]
Thus, the projection of A on B is:
[
text{proj}_B A