Introduction to Three Dimensional Geometry

JEE Main 2024 (Online) 8th April Morning ShiftMCQMedium📈 Topic in 2% papers+4−1

Ques. 1JEE Main 2024, 8 April (Morning Shift)

Let P(x, y, z) be a point in the first octant, whose projection in the xy-plane is the point Q. Let OP = ; the angle between OQ and the positive x-axis be ; and the angle between OP and the positive z-axis be , where O is the origin. Then the distance of P from the x-axis is

1 - 2 2
1 + 2 2
1 + 2 2
1 - 2 2

Answer

(1) 1 - 2 2

Solution

[figure]

(right angle at Q): z = QP = , OQ =

In the xy-plane: x = OQ =

Distance of P from x-axis = y2 + z2 = 2 - x2

= 1 - 2 2

Answer: (1)

Keep practising — Introduction to Three Dimensional Geometry

Ques. 2JEE Main 2025, 28 January (Morning Shift)

Let A(x, y, z) be a point in xy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B = (1, 4, -1) and C = (2, 0, -2). Then among the statements (S1) : ABC is an isosceles right angled triangle, and (S2) : the area of ABC is 9 22,

both are false
only (S2) is true
only (S1) is true
both are true

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