given A=i^+3j^ & B=i^+j^.find the component of vector A along B.also find the component of vector A along B
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vector A = i + 3 j magnitude = √(1+9) = √10
vector B = i + j magnitude = √2
angle between them = Ф
Cos Ф= A . B / (√10 * √2) = (1*1+3*1) / (√20) = 2/√5
Component of vector A along B is A cosФ = (i + 3 j) * 2/√5
component of vector B along A is B cos Ф = (i + j) 2/√5
vector B = i + j magnitude = √2
angle between them = Ф
Cos Ф= A . B / (√10 * √2) = (1*1+3*1) / (√20) = 2/√5
Component of vector A along B is A cosФ = (i + 3 j) * 2/√5
component of vector B along A is B cos Ф = (i + j) 2/√5
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