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Question

Match the following
ColumnIColumnII(A)The shortest distance between the lines(P)2x33=y81=z31andx+33=y+72=z64is(B)The distance of the point of intersection of the line(Q)330x23=y+14=z212and the planexy+z=5 from the point (1,5,10)is(C)The length of the perpendicular drawn from the(R)13point (5,4,1) on the linex12=y9=z5is(D)The distance between the points P and Q is d and(S)2109110the lenght of the projection of PQ on the coordinateplanes are d1,d2,d3 then d21+d22+d23=kd2 when k is

A
AR,Bq,Cs,DP
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B
Aq,Br,Cs,DP
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C
Aq,Bs,Cr,DP
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D
Ap,Bs,Cr,Dq
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Solution

The correct option is B Aq,Br,Cs,DP
A. ¯r=¯a+t.¯b¯r=¯c+s¯d shortest distance between the lines = =|[¯c¯a¯b¯d]||¯bׯd|
b. (2, -1, 2) satisfies the plane
find distance between (2, -1, 2) and (-1,-5,-10)
c. Find d.r’s of A(5,4,-1) and B(1+2k,9k,5k)
((2k4)¯i+(9k4)+(5k+1)¯k).(2¯i+9¯j+5¯k)=0 find k.
d. projection of PQ on xy-plane = (x1x2)2+(y1y2)2
projection of PQ on yz-plane = (y1y2)2+(z1z2)2
projection of PQ on zx-plane = (x1x2)2+(z1z2)2

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