321.

Find the coordinates of the point, where the line  intersects the plane . Also find the angle between the line and the plane. 

Find the vector equation of the plane which contains the line of intersection of the planes.  and  and which is perpendicular to the plane 

Find the vector equation of the plane passing through three points with position vectors  Also, find the coordinates of the point of intersection of this plane and the line 

If  are mutually perpendicular vectors of equal magnitudes, show that the vector  is equally  inclined to Also, find the angle which  with .

Find the magnitude of each of the two vectors $\overrightarrow{\mathrm{a}} \mathrm{and} \overrightarrow{\mathrm{b}}$, having the same magnitude such that the angle between them is 60^o and their scalar product is 9/2.

If θ is the angle between two vectors $\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}} \mathrm{and} 3\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + \hat{\mathrm{k}}$ find sin θ.

Let $\overrightarrow{\mathrm{a}} = 4\hat{\mathrm{i}} + 5\hat{\mathrm{j}} - \hat{\mathrm{k}} , \overrightarrow{\mathrm{b}} = \hat{\mathrm{i}} - 4\hat{\mathrm{j}} + 5\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}} = 3\hat{\mathrm{i}} + \hat{\mathrm{j}}- \hat{\mathrm{k}}$. Find a vector $\overrightarrow{\mathrm{d}}$ which perpendicular to both  $\overrightarrow{\mathrm{c}} \mathrm{and} \overrightarrow{\mathrm{b}} \mathrm{and} \overrightarrow{\mathrm{d}}. \overrightarrow{\mathrm{a}} = 21$

Find a unit vector in the direction of  $\overrightarrow{\mathrm{a} }= 3\widehat{\mathrm{i} } - 2\hat{\mathrm{j}} + 6\mathrm{k}$

Find the angle between the vectors $\overrightarrow{\mathrm{a}} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}} \mathrm{and} \overrightarrow{\mathrm{b}} = \hat{1} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$