Consider the vector `2hati+2hatj-3hatk` .Find the equation of line passing through A(3.4,5) and parallel to given vector , in the vector form and in the Cartesian form.

Find the vector and cartesian equation of the line through the point (3, -4, -2) and parallel to the vector 9hati+6hatj+2hatk .

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3hati+2hatj-2hatk .

Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane vecr.(hati+2hatj-5hatk)+9=0

Find the vector and cartesian equations of the straight line passing through (-5, 2, 3) and (4, -3, 6).

Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3hati+2hatj-8hatk .

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6 .

Find the vector equation and cartesian equation of the line through the point (1, 2, -2) and in parallel to (3hati-4hatj+5hatk) .

The vector equation of the plane through the point (2,1,-1) and parallel to the plane vecr.(hati+3hatj-hatk)=0 is

Given the vector equation of a line as vecr=(2hati-hatj+3hatk)+t(hati-hatj-hatk) find the direction cosines of the line. Find also the equation of the line in non parametric form and in cartesian form.

Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight lines vecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk) and vecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)