Decompose the vector b=6i-3j-6k into two vectors c and d,one of which is parallel and the other is perpendicular to the vector c=i+j+k.

Asked by DIPTI PRIYA | 13th Oct, 2010, 03:28: PM

Expert Answer:

Dear student,
Given vector : 6i-3j-6k
Let 6i-3j-6k = c + d, where c is parallel to i+j+k and d is perpendicular to i+j+k
hence c = m(i+j+k) where m is a scalar
         d = a1i + a2j +a3k where d.(i+j+k)=0, so a1+a2+a3=0
Now 6i-3j-6k = m(i+j+k) + (a1i +a2j +a3k)
So equating coefficients, 6 = m+a1
                                 -3 = m+ a2
                                 -6 = m+ a3
But a1+a2+a3=0 so m =-1
then a1= 7; a2 = -2 ; and a3 = -5
  6i-3j-6k = c+d = m(i+j+k) + (a1i +a2j +a3k)
                       = -1(i+j+k) + (7i-2j-5k) 
We hope this clarifies your query,
Team Topper Learning

Answered by  | 13th Oct, 2010, 05:09: PM

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