Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Write the equation of a plane which is at a distance of \[5\sqrt{3}\] units from origin and the normal to which is equally inclined to coordinate axes.

The vector equation of the plane containing the line \[\vec{r} = \left( - 2 \hat{i} - 3 \hat{j}  + 4 \hat{k}  \right) + \lambda\left( 3 \hat{i}  - 2 \hat{j}  - \hat{k}  \right)\] and the point  \[\hat{i}  + 2 \hat{j}  + 3 \hat{k} \]  is 

The equation of the plane parallel to the lines x − 1 = 2y − 5 = 2z and 3x = 4y − 11 = 3z − 4 and passing through the point (2, 3, 3) is

If the line drawn from (4, −1, 2) meets a plane at right angles at the point (−10, 5, 4), find the equation of the plane.

Find the equation of the plane which bisects the line segment joining the points (−1, 2, 3) and (3, −5, 6) at right angles.

Find the vector and Cartesian equations of the plane that passes through the point (5, 2, −4) and is perpendicular to the line with direction ratios 2, 3, −1.

If O be the origin and the coordinates of P be (1, 2,−3), then find the equation of the plane passing through P and perpendicular to OP.

Find the value of λ for which the following lines are perpendicular to each other `("x"-5)/(5λ+2) = (2 -"y")/(5) = (1 -"z")/(-1); ("x")/(1) = ("y"+1/2)/(2λ) = ("z" -1)/(3)`

hence, find whether the lines intersect or not

Find the position vector of the point which divides the join of points with position vectors `vec"a" + 3vec"b" and vec"a"- vec"b"` internally in the ratio 1 : 3. 

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors `vec"OP" = 2vec"a" + vec"b"` and `vec"OQ" = vec"a" - 2vec"b"`, respectively, in the ratio 1:2 internally

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors `vec"OP" = 2vec"a" + vec"b"` and `vec"OQ" = vec"a" - 2vec"b"`, respectively, in the ratio 1:2 externally

The position vector of the point which divides the join of points with position vectors `vec"a" + vec"b"` and 2`vec"a" - vec"b"` in the ratio 1:2 is ______.

The position vector of the point which divides the join of points `2vec"a" - 3vec"b"` and `vec"a" + vec"b"` in the ratio 3:1 is ______.

Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).

Find the image of the point (1, 6, 3) in the line `x/1 = (y - 1)/2 = (z - 2)/3`.

The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by ______.

Prove that the lines x = py + q, z = ry + s and x = p′y + q′, z = r′y + s′ are perpendicular if pp′ + rr′ + 1 = 0.

Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.