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Question

Let the foot of perpendicular from a point P(1,2,1) to the straight line L:x1=y0=z1 be N. Let a line be drawn from P parallel to the plane x+y+2z=0 which meets L at point Q. If α is the acute angle between the lines PN and PQ, then cosα is equal to

A
32
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B
123
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C
13
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D
15
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Solution

The correct option is C 13

L:x1=y0=z1=r
N(r1,0,r1)
P(1,2,1)
D.R's of NP=(r11,2,r1+1) with D.R's (1,0,1)
r11+0+r11=0
r1=1
N(1,0,1)
Q(r2,0,r2)
D.R's of normal of plane x+y+2z=0 are (1,1,2)
D.R's of PQ=(r21,2,r2+1) are perpendicular to (1,1,2)
r2122r2+2=0
r2=1
Q(1,0,1)
NP=2, PQ=23
cosα=NPPQ=13

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