PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the distance of the point (3, 3, 3) from the plane \[\vec{r} \cdot \left( 5 \hat{i}  + 2 \hat{j}  - 7k \right) + 9 = 0\]

If the product of the distances of the point (1, 1, 1) from the origin and the plane x − y + z+ λ = 0 be 5, find the value of λ.

Find the distance between the point (7, 2, 4) and the plane determined by the points A(2, 5, −3), B(−2, −3, 5) and C (5, 3, −3). 

Find the distance of the point (1, -2, 4) from plane passing throuhg the point (1, 2, 2) and perpendicular of the planes x - y + 2z = 3 and 2x - 2y + z + 12 = 0 

Find the distance between the parallel planes 2x − y + 3z − 4 = 0 and 6x − 3y + 9z + 13 = 0.

Find the distance between the planes \[\vec{r} \cdot \left( \hat{i}  + 2 \hat{j}  + 3 \hat{k}  \right) + 7 = 0 \text{ and } \vec{r} \cdot \left( 2 \hat{i}  + 4 \hat{j}  + 6 \hat{k}  \right) + 7 = 0 .\]

The distance between the planes 2x + 2y − z + 2 = 0 and 4x + 4y − 2z + 5 = 0 is 

The image of the point (1, 3, 4) in the plane 2x − y + z + 3 = 0 is

The distance of the line \[\vec{r} = 2 \hat{i} - 2 \hat{j} + 3 \hat{k} + \lambda\left( \hat{i} - \hat{j}+ 4 \hat{k}  \right)\]  from the plane \[\vec{r} \cdot \left( \hat{i} + 5 \hat{j} + \hat{k} \right) = 5\] is

If a plane passes through the point (1, 1, 1) and is perpendicular to the line \[\frac{x - 1}{3} = \frac{y - 1}{0} = \frac{z - 1}{4}\] then its perpendicular distance from the origin is ______.

\[\text{ If } \vec{a} = \hat { i }  + 3 \hat { j }  - 2 \hat { k } \text{ and }  \vec{b} = - \hat { i }  + 3 \hat { k }   , \text{ find }  \left| \vec{a} \times \vec{b} \right| .\]

If \[\vec{a} = 3 \hat { i } + 4 \hat { j } \text{ and }  \vec{b} = \hat { i  } + \hat{ j }  + \hat{ k } ,\]  find the value of \[\left| \vec{a} \times \vec{b} \right| .\]

If \[\vec{a} = 2 \hat{ i } + \hat{ k }  , \vec{b} = \hat { i }  + \hat{ j } + \hat{ k }  ,\]  find the magnitude of  \[\vec{a} \times \vec{b} .\]

 Find a unit vector perpendicular to both the vectors  \[4 \hat{ i } - \hat{ j }  + 3 \hat{ k } \text{ and }  - 2 \hat{ i  } + \hat{ j }  - 2 \hat{ k }  .\]