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

Find the vector equation of a lin e passes through the point whose position vector is (2hati-hatj-hatk) and parallel to vector hati+5hatk .

Find the equation of a line : passing through the point vec c , parallel to the plane vec r *vec n = p and intersecting the line vec r =vec a + t vec b .

Find the vector equation of a line parallel to the vector 2hati-hatj+2hatk and passing through a point A with position vector 3hati+hatj-hatk .

The vector equation of the plane passing through the origin and the line of intersection of the planes vec rdot vec a=lambdaa n d vec rdot vec b=mu is (a) vec rdot(lambda vec a-mu vec b)=0 (b) vec rdot(lambda vec b-mu vec a)=0 (c) vec rdot(lambda vec a+mu vec b)=0 (d) vec rdot(lambda vec b+mu vec a)=0

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

Find the position vector of a point which divides the join of points with position vectors vec a-2 vec b and 2 vec a+ vec b externally in the ratio 2:1.

Let vec n be a vector of magnitude 2sqrt(3) such that it makes equal acute angles with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane passing through (1,-1,2) and normal to vec ndot

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2\ vec a+ vec b) and ( vec a-\ 3 vec b) respectively, externally in the ratio 1:2.Also, show that P is the mid-point of the line segment R Qdot

Prove that the normal to the plane containing three points whose position vectors are vec a , vec b , vec c lies in the direction vec bxx vec c+vec cxx vec a+ vec axx vec bdot

The position vector of the point which divides the line segment joining the points with position vectors 2 vec(a) = 3b and vec(a) + vec(b) in the ratio 3:1 is