if f bar equals to 3 i cap+ 4 j cap - 5 k cap and d bar equals to 5 i cap + 4 j cap + 3 k cap then find the projection of F bar on d bar
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it is given that,
f = 3i + 4j - 5k and d = 5i + 4j + 3k
we have to find the projection of f on d.
we know, if a and b two vectors are given then, projection of a on b = a.b/|b|
so, projection of f on d = f.d/|d|
= (3i + 4j - 5k).(5i + 4j + 3k)/|5i + 4j + 3k|
= {3 × 5 + 4 × 4 + (-5) × 3}/√{(5)² + (4)² + (3)²}
= (15 + 16 - 15)/√{25 + 16 + 9}
= 14/√50
= 14/(5√2)
hence, projection of f on d is 14/(5√2).
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