Question Solved1 Answer Knowledge/Understanding (15 marks) 1. If ū= [1.-3,-2) and 1 = [4.–5,3] find: a) 2 - 3 121 b) u + 1-5/1 c) Find Q, where P (-7,5,-1) and PQ = 2 [31 d) Find w which is orthogonal to both ü & v [3]

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Transcribed Image Text: Knowledge/Understanding (15 marks) 1. If ū= [1.-3,-2) and 1 = [4.–5,3] find: a) 2 - 3 121 b) u + 1-5/1 c) Find Q, where P (-7,5,-1) and PQ = 2 [31 d) Find w which is orthogonal to both ü & v [3]
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Transcribed Image Text: Knowledge/Understanding (15 marks) 1. If ū= [1.-3,-2) and 1 = [4.–5,3] find: a) 2 - 3 121 b) u + 1-5/1 c) Find Q, where P (-7,5,-1) and PQ = 2 [31 d) Find w which is orthogonal to both ü & v [3]
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Sol. (1) (a) 2 vec(u)-3 vec(u)=[2,-6,-4]-[12,-15,9]=[-10,9,-13]" (b) "{:[ vec(u)+ vec(k)-5 hat(ȷ)= hat(ı)-3 hat(ȷ)-2 hat(k)+4 hat(ı)-5 hat(ȷ)+3 hat(k)-5 hat(ȷ)],[=5 hat(ı)-13 hat(ȷ)+ hat(k)],[| vec(u)+ vec(v)-5 hat(ȷ)|=sqrt(25+169+1)=sqrt195]:}(C) vec(PQ)=2 vec(u){:[ vec(OQ)- vec(OP)=2 vec(U)", where "O" is ongin "],[ vec(OQ)= vec(OP)+2 vec(u)],[ vec ... See the full answer