Q.No.1 Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4) and R(6,-2,-5) is right-angled.
Let us find the coordinates of the vectors "\\overrightarrow{QP}" and "\\overrightarrow{QR}:"
"\\overrightarrow{QP}=(1-2,-3-0,-2-(-4))=(-1,-3,2)"
"\\overrightarrow{QR}=(6-2,-2-0,-5-(-4))=(4,-2,-1)"
Since the scalar product "\\overrightarrow{QP}\\cdot\\overrightarrow{QR}=4(-1)-3(-2)+2(-1)=-4+6-2=0" , we conclude that "\\angle PQR=90^\\circ", and therefore the triangle with vertices "P(1,-3,-2), Q(2,0,-4)" and "R(6,-2,-5)" is right-angled.
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