If a,b,care mutually perpendicular vectors of equal magnitudes, show that the vector a+b+cis equally inclined to a,b and c.
Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.
If the vectors i^−j^,j^+k^anda form a triangle, then a may be a. −i^−k^ b. i^−2j^−k^ c. 2i^+j^+k^ d. i^+k^
Statement 1: if three points P,QandR have position vectors a,b,andc , respectively, and 2a+3b−5c=0, then the points P,Q,andR must be collinear. Statement 2: If for three points A,B,andC,AB=λAC, then points A,B,andC must be collinear.
If a,bandc are non-coplanar vectors, prove that the four points 2a+3b−c,a−2b+3c,3a+ 4b−2canda−6b+6c are coplanar.
If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.