If a line has direction -ratios<2,-1,-2>,determine its direction cosines.

3

(a)

Find the direction cosines of the line passing through the two points (-2, 4, -5) and (1, 2, 3)

3

(a)

Find the direction-cosines of x, y and z-axis.

3

(a)

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

3

(a)

Find the distance of a point (2, 5, - 3) from the plane:
\(\hat { r } .(6\hat { i } -3\hat { j } +2\hat { k }) =4\)

3

(a)

If a line has the direction ratios -18, 12, -4 then what are its direction cosines?

3

(a)

Find the intercepts cut off by the plane: 2x + y - z = 5 with the axes.

3

(a)

Find the equation of the line parallel to x-axis and passing through the origin.

3

(a)

Find the distance of the point(-1,-5,-10) from the point of intersection of the line:
\(\vec { r } .\left( \hat { i } -\hat { j } +2\hat { k } \right) +\lambda \left( 3\hat { i } +4\hat { j } +2\hat { k } \right) \) and the plane \(\vec { r } .\left( \hat { i } -\hat { j } +\hat { k } \right) =5\)

3

(a)

Find the equation of the plane passing through the line of intersection of the planes:
\(\vec { r } .\left( \hat { i } +\hat { j } +\hat { k } \right) =1\ and \ \vec { r } .\left( 2\hat { i } +3\hat { j } -\hat { k } \right) +4=0\) and parallel to x-axis.

3

(a)

Find the shortest distance between lines:
\(\vec { r } =6\hat { i } +2\hat { j } +2\hat { k } +\lambda (\hat { i } -2\hat { j } +2\hat { k } )and\\ \vec { r } =-4\hat { i } -\hat { k } +\mu (3\hat { i } -2\hat { j } -2\hat { k } )\)

3

(a)

Find the equation of the line passing through (a,b,c) and parallel to the plane \(\vec { r } =(\hat { i } +\hat { j } +\hat { k } )=2\)

3

(a)

Find the shortest distance between the two lines whose vector equations are:
\(\vec { r } =\hat { i } +2\hat { j } +3\hat { k } +\lambda (\hat { i } -3\hat { j } +2\hat { k } )and\)
\(\vec { r } =(4\hat { i } +5\hat { j } +6\hat { k } )+\mu (2\hat { i } +3\hat { j } +\hat { k } )\)

3

(a)

Find the shortest distance between the lines
\(\vec { r } =\hat { (i } +2\hat { j } +\hat { k } )+\lambda (\hat { i } -\hat { j } +\hat { k } )and\)
\(\vec { r } =(2\hat { i } -\hat { j } -\hat { k } )+\mu (2\hat { i } +\hat { j } +2\hat { k } )\)

3

(a)

Find the vector and cartesian equation of the line that passes through the origin and (5,-2,3).

3

(a)