NDA Mathematics 3 September 2023 | Three Dimensional Geometry Question 5 | Mathematics

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

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?

0°

30°

60°

90°

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

What is the equation of the sphere concentric with the sphere x2 + y2 + z2 - 2x - 6y -8z - 5 = 0 and which passes through the origin?

x2 + y2 + z2 - 2x - 8z = 0

x2 + y2 + z2 - 2x - 6y = 0

x2 + y2 + z2 - 6y - 8z = 0

x2 + y2 + z2 - 2x - 6y - 8z = 0

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