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

Write the vectorthe 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

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

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

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane vec rdot((2 hat i+ hat j+2 hat k)=5.

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

(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)) .

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