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NCERT Class XII Mathematics Chapter - - Solutions

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Question 35 - 38: In the following cases, find the coordinates of the foot of theperpendicular drawn from the origin.
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Question : 38 of 78
Marks: +1, -0
5y + 8 = 0
Solution:  
Let the coordinates of the foot of the perpendicular P from the origin to the plane be (x1,y1,z1)(x_1, y_1, z_1) .
Then the direction ratios of the line OP are x1,y1,z1x_1, y_1, z_1.
Writing the equation of the plane in the normal form, we have 0x+55y+0z=850x+\frac{5}{5}y+0z=-\frac{8}{5}
where 0, 1, 0 are the direction cosines of OP.
Since direction cosines and direction ratios of a line are proportional, then x10=y11=z10=k\frac{x_1}{0}=\frac{y_1}{1}=\frac{z_1}{0}=k
i.e. x1=0,y1=k,z1=0x_1 = 0, y_1 = k, z_1 = 0
Substituting these values in the equation of the plane, we get k=85.k=-\frac{8}{5}.
Hence the foot of perpendicular is (0,85,0).\left(0,-\frac{8}{5},0\right).
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