Embibe Experts Solutions for Chapter: Three Dimensional Geometry, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

What is the length of the diameter of the sphere whose centre is at $(1, -2, 3)$ and which touches the plane $6x-3y+2z-4=0?$

What is the perpendicular distance from the point $(2, 3, 4)$ to the line $\frac{x-0}{1}=\frac{y-0}{0}=\frac{z-0}{0}?$

Into how many compartments do the coordinate planes divide the space?

What is the equation of the plane which cuts an intercept $5$ units on the $Z$-axis and is parallel to $XY$-plane?

A point on the line $\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+2}{7}$ has coordinates

If the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies on the plane $2 x-4 y+z=7,$ then what is the value of $k?$

A straight line passes through the point $\left(1, 1, 1\right)$ makes an angle $60°$ with the positive direction of $Z$-axis, and the cosine of the angles made by it with the positive directions of the $Y$-axis and the $X$-axis are in the ratio $\sqrt{3} : 1.$ What is the acute angle between the two possible positions of the line?

If the points $A\left(x, y, -3\right), B\left(2, 0, -1\right)$ and $C\left(4, 2, 3\right)$ lie on a straight line, then what are the values of $x$ and $y$ respectively?