Exams › JEE Main › Maths

If a point R(4, y, z) lies on the line segment joining the points P(2, -3, 4) and Q(8, 0, 10), then the distance of R from the origin is -

1. 6
2. √53
3. 2√14
4. 2√21

Correct answer: 2√14

Solution

The point R lies on the line segment between P and Q, which means its coordinates can be expressed as a weighted average of P and Q. By calculating the coordinates of R, we find that R(4, -1, 7) results in a distance from the origin of 2√14, confirming that this is the correct option.

Related JEE Main Maths questions

• A line makes equal angles α, β and γ with the positive directions of the coordinate axes. If θ satisfies cos θ = (cos²α + cos²β + cos²γ) / (sin²α + sin²β + sin²γ), then what is the value of θ?
• A rectangular box is bounded by planes passing through the points (-1, 2, 5) and (1, -1, -1), each plane being parallel to one of the coordinate planes. What is the length of the space diagonal of this box?
• If (2, 3, 5) is one end of a diameter of the sphere x² + y² + z² - 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are
• The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point (0, 17/2, -13/2). Then
• Q.65 Let PQR be a triangle with R(-1, 4, 2). Suppose M (2, 1, 2) is the mid-point of PQ. The distance of the centroid of ΔPQR from the point of intersection of the lines (x−2)/0 = y/2 = (z+3)/(−1) and (x−1)/1 = (y+3)/(−3) = (z+1)/1 is-
• A line passes through A(4, -6, -2) and B(16, -2, 4). The point P(a, b, c), where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, -12, 3) is equal to ____

⚔️ Practice JEE Main Maths free + battle 1v1 →