InterviewSolution
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InterviewSolution
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The vector component of vector `vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k)` along vector `vec(B) = hat(i) + hat(j) + hat(k)` isA. `2 hat (i) + 2 hat(j) + 2 hat(k)`B. `3 hat (i) + 3 hat(j) + 3 hat(k)`C. `4 hat (i) + 4 hat(j) + 4 hat(k)`D. `5 hat (i) + 5 hat(j) + 5 hat(k)` |
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Answer» Correct Answer - C Vector component of `vec(A) along vec(B)` is `{|vec(A)| cos theta|} hat(B) = ( vec(A) . hat(B)) hat(B)` `hat(B) = (vec(B))/(|vec(B)|) = ( i + j + k)/(sqrt( 1 + 1 +1)) = ( i + j + k)/(sqrt(3))` `vec(A) . hat(B) = ( 3 i + 4 j + 5 k).((i + j + k)/(sqrt(3)))` `= ( 3 + 4 + 5)/(sqrt(3)) = (12)/(sqrt(3))` `(vec(A) . hat(B)) hat(B) = ((12)/(sqrt(3))) ( i + j + k)/(sqrt(3)) = 4 ( i + j + k)` |
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