    Question

# The projection of a line segment joining the points P(x1,y1,z1,) and Q(x1,y1,z1,) on another line whose DC's are l,m,n is given by

A
l(x1+x2)+m(y2+y2)+n(z1+z2)
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B
2[(lx2+my2+nz2)2(lx1+my1+nz1)2]
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C
l(x2x1)+m(y2y1)+n(z2z1)
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D
x2x1l+y2y1m+z2z1n
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Solution

## The correct options are B 2[(lx2+my2+nz2)2−(lx1+my1+nz1)2] C l(x2−x1)+m(y2−y1)+n(z2−z1)Let the line be of length PD.R.'s of line are x2−x1P,y2−y1P,z2−z1PD.C.'s of line on which project is taken is (l,m,n)So, projection =P[(D.R. of line).(D.R. of line on which project is taken)]P[x2−x1P⋅l+y2−y1P⋅m+z2−z1P⋅n]=(x2−x1)l+(y2−y1)m+(z2−z1)n ie option C=x2l+y2m+z2n−x1l−y1m−z1n=x2l+y2m+z2n−(x1l+y1m+z1n)=2(x2l+y2m+z2n−(x1l+y1m+z1n)2)=2(x2l+y2m+z2n2−x1l+y1m+z1n2)ie Option B   Suggest Corrections  0      Similar questions  Related Videos   Direction Cosines and Direction Ratios
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