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Find the coordinates of the foot of the perpendicular from the point (2, 3, 7) to the plane 3x − y − z = 7. Also, find the length of the perpendicular.
Concept: undefined >> undefined
Find the image of the point (1, 3, 4) in the plane 2x − y + z + 3 = 0.
Concept: undefined >> undefined
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Find the length and the foot of the perpendicular from the point (1, 1, 2) to the plane \[\vec{r} \cdot \left( \hat{i} - 2 \hat{j} + 4 \hat{k} \right) + 5 = 0 .\]
Concept: undefined >> undefined
Find the coordinates of the foot of the perpendicular and the perpendicular distance of the point P (3, 2, 1) from the plane 2x − y + z + 1 = 0. Also, find the image of the point in the plane.
Concept: undefined >> undefined
Find the direction cosines of the unit vector perpendicular to the plane \[\vec{r} \cdot \left( 6 \hat{i} - 3 \hat{j} - 2 \hat{k} \right) + 1 = 0\] passing through the origin.
Concept: undefined >> undefined
Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x − 3y + 4z − 6 = 0.
Concept: undefined >> undefined
Find the length and the foot of perpendicular from the point \[\left( 1, \frac{3}{2}, 2 \right)\] to the plane \[2x - 2y + 4z + 5 = 0\] .
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
Write the equation of the plane parallel to XOY- plane and passing through the point (2, −3, 5).
Concept: undefined >> undefined
Write the equation of the plane parallel to the YOZ- plane and passing through (−4, 1, 0).
Concept: undefined >> undefined
Write the equation of the plane passing through points (a, 0, 0), (0, b, 0) and (0, 0, c).
Concept: undefined >> undefined
Write the general equation of a plane parallel to X-axis.
Concept: undefined >> undefined
Write the value of k for which the planes x − 2y + kz = 4 and 2x + 5y − z = 9 are perpendicular.
Concept: undefined >> undefined
Write the intercepts made by the plane 2x − 3y + 4z = 12 on the coordinate axes.
Concept: undefined >> undefined
Write the ratio in which the plane 4x + 5y − 3z = 8 divides the line segment joining the points (−2, 1, 5) and (3, 3, 2).
Concept: undefined >> undefined
Write the distance between the parallel planes 2x − y + 3z = 4 and 2x − y + 3z = 18.
Concept: undefined >> undefined
Write the distance of the plane \[\vec{r} \cdot \left( 2 \hat{i} - \hat{j} + 2 \hat{k} \right) = 12\] from the origin.
Concept: undefined >> undefined
Write the equation of the plane \[\vec{r} = \vec{a} + \lambda \vec{b} + \mu \vec{c}\] in scalar product form.
Concept: undefined >> undefined
Write the equation of the plane passing through (2, −1, 1) and parallel to the plane 3x + 2y −z = 7.
Concept: undefined >> undefined
Write the equation of the plane containing the lines \[\vec{r} = \vec{a} + \lambda \vec{b} \text{ and } \vec{r} = \vec{a} + \mu \vec{c} .\]
Concept: undefined >> undefined
