Question

Three vectors A,B,and C are related to one another such that
5A + 6B = 60C. A fourth vector D
exists such that 30C + D = A.
Determine an expression for D in terms of the vectors A and B.
1st: equation1: 5A+6B=60C equation2: 30C+D=A
2nd: divide equation1 by2-->((5A+6B=60C)/2)=5/2A+6/2B=30C now reduce itto 5/2A+3B=30C
3rd: subtract30C on both side of the equal sign on equation2 and get: D=A-30C
4th:subtitute for equation1 into the Nnew equation2 30C--> D=A-[5/2A+3B]
5th: distribute the negative sign and get-->D=A-5/2A-3B-->2/2A-5/2A-3B
6th: answer: -3/2A-3B

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