Find the vector equation of a plane through the point `hati+ hat j+hat k` and parallel to the plane `vecr.(2 hat i-hatj +2 hatk)=5`.

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

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r.( hat i- hat j+2 hat k)=5a n d vec r.(3 hat i+ hat j+ hat k)=6.

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to the plane 3x-4y+5z=8.

Find the equation of a plane through the intersection of the planes vecr.(hati+3hat j-hat k)=5 and vecr.(2hat i-hatj +hatk)=3 and passing through the point (2,1,-2)

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

(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 line passing through the point (2,-1,3) and parallel to the line vec(r)=(hat(i)-2hat(j)+hat(k))+lamda(2hat(i)+3hat(j)-5hat(k))

Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3hat(i)+2hat(j)-8hat(k) .

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the unit vector perpendicular to the plane vec r.(2 hat i+ hat j+2 hat k)=5.