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# Lecture - 10 Chapter 11 Three Dimensional Geometry

**2.** Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector \(3\hat{i}+5\hat{j}-6\hat{k}\).

**12.** Find the vector equation of the plane which is at a distance of \(\frac{6}{\sqrt{29}}\) from the origin and its normal vector from the origin is \(2\hat{i}-3\hat{j}+4\hat{k}\). Also find its cartesian form.

**13.** Find the direction cosines of the unit vector perpendicular to the plane \(\vec{r}.(6\hat{i}-3\hat{j}-2\hat{k})+1=0\) passing through the origin.

**14.** Find the distance of the plane 2x-3y+4z-6=0 from the origin.

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