Find the vector and the Cartesian equations of the line through the point (5, 2, – 4) and which is parallel to the vector `3hati+2hatj-8hatk`

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

Find the vector and cartesian equations of the plane that passes through the point (1, 0, – 2) and the normal to the plane is hati+hatj-hatk

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Write the cartesian equation of the straight line through the point (1,2,3) and along the vector 3hati+hatj+2hatk

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

Find the vector and cartesian equations of the plane that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

Find a vector of magnitude (5/2) units which is parallel to the vector 3hati+4hatj .

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .