If a line passing through the point with position vector `vec(alpha)` and parallel to vector `vec(beta)` then the vector equation of the line is-

Obtain the equation of a line passing through a point A with Position vector vec(a) and parallel to a vector vec(b) both in vector and cartesion form.

A line passes through the point A(5,-2.4) and it is parallel to the vector (2hat(i) -hat(j) +3hat(k)) .The vector equations of the line is

Find the vector and cartesian equations of the straight line passing through the point A with position vector 3veci-vecj+4veck and parallel to the vector -5veci+7vecj+3veck .

Write the vector equation of a line passing through a point having position vector vec alpha\ a n d parallel to vec A Bdot

P is a point on the line through the point A whose position vector is vec a and the line is parallel to the vector vec b . If P A=6, the position vector of P is: (a) vec a+6 vec b (b) vec a+6/(| vec b|) vec b (c) vec a-6 vec b/(| vec b|) (d) vec b+6/(| vec a|) vec a

P is a point on the line through the point A whose position vector is vec a and the line is parallel to the vector vec b. If PA=6, the position vector of P is: (a) vec a+6vec b (b) vec a+(6)/(|vec b|)vec b(c)vec a-6(vec b)/(|vec b|) (d) vec b+(6)/(|vec a|)vec a

Find the vector equation of the line passing through the point with position vector 2 hati - hatj + hatk and parallel to the line joining the points with position vectors - hati + 4hatj + hatk and hati + 2 hatj + 2 hatk . Also, find the cartesian equation of the line.

Derive the equation of a line in 3D passing through two points A and B with position vectors vec(a) " and " vec(b) respectively both in vector and Cartesian form.

Show that equation of the plane passing through a point having position vector vec(a) and parallel to vec(b) and vec(c) is vec(r) = vec(a) + lambda vec(b) + mu vec(c) .