The Cartesian equation of the line passing through the point `2i -j +4k` and parallel to the vector `i+j-2k` is

The Cartesian equation of the plane passing through the point (3,-2,-1) and parallel to the vectors vec b=i-2j+4k and vec c=3i+2j-5k

Equation of the plane passing through the origin, and parallel to the vectors i+3j -k and j+k, is

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

The vector equation of the line passing through the point i-2j+k and perpendicular to the vectors 2i-3j-k,i+4j-2k is

Find the vector and cartesian equations of the line passing through the point P(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 and Cartesian equations of the line through the point (5,\ 2,\ -4) and which is pralel to the vector 3 hat i+2 hat j-8 k dot

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.

Equation of the plane passing through the points i+j-2k,2i-j+kandi+2j+k is

The vector equation of the line passing through the point bar(i)-2bar(j)+bar(k) and perpendicular to the vectors 2bar(i)-3bar(j)-bar(k),bar(i)+4bar(j)-2bar(k) is