Three Dimensional Geometry

### Find the values of p so that the lines and are at right angles.

Solution: The standard form of a pair of Cartesian lines is:...

### Find the equation of the plane through the intersection of the planes r.(i+3j)-6=0 and r.(3i-j-4k)=0, whose perpendicular distance from origin is unity.

According to ques,

### The plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle α. Prove that the equation of the plane in its new position is Ax+by ( )z=0

According to ques, planes are: $~ax\text{ }+\text{ }by\text{ }=\text{ }0\text{ }\ldots .\text{ }\left( i \right)$ and $z\text{ }=\text{ }0\text{ }\ldots .\text{ }\left( ii \right)$ hence, the...

### Find the distance of a point (2, 4, –1) from the line (x+5)/1=(y+3)/4=(z-6)/-9

According to ques,

### If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane.

According to ques, Points are : $\left( 2,\text{ }\text{ }1,\text{ }\text{ }3 \right)\text{ }and\text{ }\left( 1,\text{ }\text{ }3,\text{ }3 \right)$ And, Direction ratios of the normal to the...