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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
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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
Write the position vector of the point where the line \[\vec{r} = \vec{a} + \lambda \vec{b}\] meets the plane \[\vec{r} . \vec{n} = 0 .\]
Concept: undefined >> undefined
Write the intercept cut off by the plane 2x + y − z = 5 on x-axis.
Concept: undefined >> undefined
Find the length of the perpendicular drawn from the origin to the plane 2x − 3y + 6z + 21 = 0.
Concept: undefined >> undefined
Find the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane \[\vec{r} . \left( \hat{i} + \hat{j} + \hat{k} \right) = 2\]
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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
Concept: undefined >> undefined
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
Concept: undefined >> undefined
Find a vector of magnitude 26 units normal to the plane 12x − 3y + 4z = 1.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
