Q. 75.0( 2 Votes )

Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Answer :

Given: points are A(3, 4, 1) and B(5, 1, 6)


To find: the coordinates of the point where the line passing through the given points crosses the XZ plane and angle which it make with the plane


Formula used:




Here A = (3, 4, 1)



and B = (5, 1, 6)










On comparing,


x = 3 + 2λ, 0 = 4 – 3λ, z = 1 + 5λ


0 = 4 – 3λ




x = 3 + 2λ






z = 1 + 5λ






Hence, the coordinates of the point where the line passing through the given points crosses the XZ plane is,



Formula used:





Here,






Therefore,









Hence, angle between the line and XZ plane is,



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