Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector `3 hat i+2 hat j-2 hat k`.

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3hat i+2hat j-2hat k

Find the vector equation for the line which passes through the point (1, ,2 3) and parallel to the vector hat i-2 hat j+3 hat kdot reduce the corresponding equation in the Cartesian from.

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

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

Find the vector equation of a line through the point (5, 2, -4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8hatk ?

Find the equartion of the line in vector form passing through the point ( 4 , -2,5) and parrallel to the vector 3 hat(i) + hat(j) + 2 hat(k) .

Find the vector and the 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 and Cartesian forms of the equation of the plane passing through the point (1,\ 2,\ -4) and parallel to the lines vec r=( hat i+2 hat j-4 hat k)+lambda(2 hat i+3 hat j+6 hat k)a n d\ vec r=( hat i-3 hat j+5 hat k)+mu( hat i+ hat j- hat k)dot Also find the distance of the point (9, -8, -10) from the plane thus obtained.

(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