Current location - Training Enrollment Network - Mathematics courses - Questions about mathematical vectors: OB vector =a times OA vector +b times OC vector. If AB and C are collinear, how to prove that a+b= 1? Ask for advice, be specific.
Questions about mathematical vectors: OB vector =a times OA vector +b times OC vector. If AB and C are collinear, how to prove that a+b= 1? Ask for advice, be specific.
By vector OB=a vector OA+b vector OC,

When a, b, C*** lines,

There is a real number n, so vector AB=n vector AC,

That is, vector OB- vector OA=n (vector OC- vector OA)

Vector OB- vector OA=n vector OC-n vector OA

Vector OB=( 1-n) vector OA+n vector oc,

Where: a= 1-n and b = n.

a+b= 1。