Balance on a bicycle is a matter of constantly correcting against falls, and it's easier when the speed is higher because the inertia of moving forward overcomes the need for corrective actions.
If a vector A is multiplied by a real number (say n), the vector of same nature is obtained but its magnitude is n times that of A.
This picture develops a clear understanding.
No, if three vectors do not lie in a plane, they cannot give zero resultant.
Explanation:
Let A, B and C be three vectors. If they give zero resultant, then
A+B+C=0
or, A= -(B+C)
Hence, they will produce zero resultant, if A is equal to negative of vector (B+C). The vector (B+C) lies in the plane of B and C. Hence, A will be equal to negative of (B+C) if A, B and C all lie in a plane.
