Find the vector equation of plane which passes through the point `A(1,-1,1)` and perpendicular to the vector `4hat i+2hat j+2hat k`

Find the equation of the plane passing through the point A=(3,-2,-1) and perpendicular to the vactors vec b=hat i-2hat j-4hat k,vec c=3hat i+2hat j-5hat k

Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane vec r*(hat i+2hat j-5hat k)+9=0

Write the vector equation of the plane passing through the point (a,b,c) and parallel to the plane vec r.(hat i+hat j+hat k)=2

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

Find the vector and Cartesian equations of a plane which passes through the point (1,4,6) and normal vector to the plane is (hat i-2hat j+hat k)

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

Write the vector equation of the plane,passing through the point (a,b,c) and parallel to the plane vec r*(hat i+hat j+hat k)=2

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

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the non-parametric equation of a line passing through (1,2,3) and perpendicular to the vectors (5hat i-3hat j+4hat k) and (-7hat i+4hat j+9hat k) Or Find the equation of a straight line passing through point (1,2,3) and perpendicular to the vectors (5,-3,4) and (-7,4,9).