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

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

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Correct answer: C. 1 3

Let x 1 = y 0 = z -1 = N ( , 0,- ) b = i - k PN b =0 1(1- )-( -1)=0 =1 N (1,0,-1) Let Q ( , 0,- ) n = i + j +2 k Now, PQ n =0 =-1 Q (-1,0,1) PN =2 j and PQ =2 i +2 j -2 k = 1 3

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

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