NDA Mathematics 21 April 2024 | Three Dimensional Geometry Question 3 | Mathematics

A line through $(1, −1, 2)$ with direction ratios $\langle 3, 2, 2 \rangle$ meets the plane $x + 2y + 3z = 18$. What is the point of intersection of line and plane?

(4, 4, 1)

(2, 4, 1)

(4, 1, 4)

(3, 4, 7)

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

If $p$ is the perpendicular distance from origin to the plane passing through $(1, 0, 0)$, $(0, 1, 0)$ and $(0, 0, 1)$, then what is $3p^2$ equal to?

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

If L is the line with direction ratios < 3, -2, 6 > and passing through (1, -1, 1), then what are the coordinates of the points on L whose distance from (1, -1, 1) is 2 units?

$\left(-\frac{11}{7}, \frac{13}{7}, \frac{19}{7}\right) $ and $\left(\frac{1}{7}, \frac{3}{7}, \frac{5}{7}\right) $

$ \left(\frac{19}{7},-\frac{11}{7}, \frac{13}{7}\right) $ and $\left(-\frac{1}{7}, \frac{3}{7},-\frac{5}{7}\right) $

$ \left(\frac{13}{7}, \frac{11}{7}, \frac{19}{7}\right) $ and $\left(-\frac{1}{7},-\frac{3}{7}, \frac{5}{7}\right) $

$\left(\frac{13}{7},-\frac{11}{7}, \frac{19}{7}\right)$ and $\left(\frac{1}{7},-\frac{3}{7},-\frac{5}{7}\right)$

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

Which one of the planes is parallel to the line $\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

2x + 2y + z - 1 = 0

2x - y - 2z + 5 = 0

2x + 2y - 2z + 1 = 0

x - 2y + z - 1 = 0

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