Find the vector equation of a line which passes throught the point with position vector`hati - 2hat j+4hatk` and is in the direction of `hati + 2hatj - hatk`. Also reduce it to cartesian form.

Find the vector equation of a line which passes through the point with position vector hat(i)-2hat(j)+4hat(k) and is in the direction of hat(i)+2hat(j)-hat(k) . Also, reduce it to cartesian from.

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find the equations of the line in vector and Cartesian forms.

Find the vector equations of the plane passing through the points 3 hati+ 4 hatj+2 hatk, 2hati-2 hatj -hatk and 7 hati+6 hatk .

The vector equation of the line passing through the point (3, -1, 2) and parallel to the vector 2hati-3hatj+4hatk is -

Find the distance of the point with position vector 2 hati+ hatj- hatk from the plane vecr .( hati- 2 hatj+ 4 hatk)=9 .

Find the vector equation of the line passing through the point (2,-3,1) and parallel to the planes vec r.(2hati-3hatj-hatk)=3 and vec r.(hati+hatj-hatk)=4 .

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Find the equation of the plane which passing through the point hati + hatj + hatk and parallel to the plane vec r.(2hati - hatj + 2hatk) = 0.

Find the equation of the plane which passing through the points hati+ hatj+ hatk and parallel to the plane vecr.(2 hati-hatj+2 hatk)=5