Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202310 May 2023Morning ShiftMathematicsStraight LinesActual

The co-ordinates of the point, where the line through A (3,4,1) and B (5,1,6) crosses the XZ -plane, are

Options

  1. A( 11 3 , 0, 21 3 )
  2. B( 17 3 , 0, 23 3 )
  3. C( -11 3 , 0, 21 3 )
  4. D( 17 3 , 0, -23 3 )

Correct answer

B. ( 17 3 , 0, 23 3 )

Step-by-step solution

Let A (x₁, y₁, z ₁ )= A (3,4,1) and B (x₂, y₂, z₂ )= B (5,1,6) The equation of the line passing through the - points (x₁^1, y₁, z₁ ) and (x₂, y₂, z₂ ) is given by aligned & x-x₁ x₂-x₁ = y-y₁ y₂-y₁ = z-z₁ z₂-z₁ & x-3 5-3 = y-4 1-4 = z-1^1 6-1 & x-3 2 = y-4 -3 = z-1 5 aligned Since the line crosses the XZ plane, y=0 aligned & x-3 2 = 4 3 = z-1 5 x-3 2 & = 4 3 and z-1 5 = 4 3 x & = 17 3 and z = 23 3 aligned The required point is ( 17 3 , 0, 23 3 ) .

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All MHT CET PYQs