Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Find the length and the foot of perpendicular from the point \[\left( 1, \frac{3}{2}, 2 \right)\]  to the plane \[2x - 2y + 4z + 5 = 0\] .

Find the equation of the plane that contains the point (1, –1, 2) and is perpendicular to both the planes 2x + 3y – 2z = 5 and x + 2y – 3z = 8. Hence, find the distance of point P (–2, 5, 5) from the plane obtained

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector \[2 \hat{i}  + 3 \hat{j}  + 4 \hat{k} \] to the plane  \[\vec{r} . \left( 2 \hat{i} + \hat{j}  + 3 \hat{k}  \right) - 26 = 0\] Also find image of P in the plane.

Find the distance of the point P (–1, –5, –10) from the point of intersection of the line joining the points A (2, –1, 2) and B (5, 3, 4) with the plane x – y + z = 5.

Write the distance of the plane  \[\vec{r} \cdot \left( 2 \hat{i} - \hat{j} + 2 \hat{k} \right) = 12\] from the origin.

Write the equation of the plane  \[\vec{r} = \vec{a} + \lambda \vec{b} + \mu \vec{c}\]   in scalar product form.

Write the equation of the plane passing through (2, −1, 1) and parallel to the plane 3x + 2y −z = 7.

Write the equation of the plane containing the lines \[\vec{r} = \vec{a} + \lambda \vec{b} \text{ and }  \vec{r} = \vec{a} + \mu \vec{c} .\]

Write the position vector of the point where the line \[\vec{r} = \vec{a} + \lambda \vec{b}\] meets the plane  \[\vec{r} . \vec{n} = 0 .\]

Find the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane \[\vec{r} . \left( \hat{i}  + \hat{j}  + \hat{k}  \right) = 2\]