THE COMPONENT OF VECTOR P=6i+2j-5k ALONG VECTOR Q3i-4j
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vector P: 6 i + 2 j - 5 k
vector Q: 3 i - 4 j
u = unit vector along Q : (3 i - 4 j ) / √(3²+4²) = 3/5 i - 4/5 j
magnitude of the component of vector P along the vector Q: P = dot product of vector P and unit vector u or Q/|Q|.
= (6 i + 2 j - 5 k) . (3/5 i - 4/5 j)
= 18/5 - 8/5 = 2
component of vector P along vector Q: 2 u = 6/5 i - 8/5 j
vector Q: 3 i - 4 j
u = unit vector along Q : (3 i - 4 j ) / √(3²+4²) = 3/5 i - 4/5 j
magnitude of the component of vector P along the vector Q: P = dot product of vector P and unit vector u or Q/|Q|.
= (6 i + 2 j - 5 k) . (3/5 i - 4/5 j)
= 18/5 - 8/5 = 2
component of vector P along vector Q: 2 u = 6/5 i - 8/5 j
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