Three Dimensional Geometry

JEE Main 2024 (Online) 27th January Evening ShiftMCQMedium📈 Topic in 71% papers+4−1

Ques. 1JEE Main 2024, 27 January (Evening Shift)

Let the image of the point (1,0,7) in the line x1= y-12= z-23 be the point ( , , ). Then which one of the following points lies on the line passing through ( , , ) and making angles 2 3 and 3 4 with y-axis and z-axis respectively and an acute angle with x-axis ?

(1,-2,1+ 2 )
(3,-4,3+2 2 )
(3,4,3-2 2 )
(1,2,1- 2 )

Answer

(3) (3,4,3-2 2 )

Solution

Foot M( ,1+2 ,2+3 ); PM ( i+2 j+3 k):

( -1)+2(2 +1)+3(3 -5)=0 14 =14 =1, M(1,3,5)

[figure]

∵ M is the mid-point of PQ: ( , , )=2M-P=(1,6,3)

m= 2 3=- 12, n= 3 4=- 1 2

l2=1- 14- 12= 14

∵ acute angle with x-axis l=+ 12

Point on line: (1+ 2, 6- 2, 3- 2 ); =4 (3,4,3-2 2 )

Answer: (3)

Keep practising — Three Dimensional Geometry

Ques. 2JEE Main 2024, 27 January (Evening Shift)

The lines x-22= y-2= z-716 and x+34= y+23= z+21 intersect at the point P. If the distance of P from the line x+12= y-13= z-11 is l, then 14l2 is equal to .

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