AP EAMCET202021 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual
Let ( u ) and ( v ) be two vectors in a plane. Then any vector ( w ) in the plane can be written as (w=a u +b v ) for some scalars ' (a ) ' and ' (b ) ' if and only if
Options
- ANone of ( u ) and ( v ) is a scalar multiple of the other
- BNone of (|u| ) and (|v| ) is a scalar multiple of the other
- C(u ) and (v ) have different direction
- D(u ) and (v ) are perpendicular to each other
Correct answer
B. None of (|u| ) and (|v| ) is a scalar multiple of the other
Step-by-step solution
Any vector ( w ) in the plane containing vector ( u ) and ( v ) can be written as ( w =a u +b v ) for some scalars ' (a ) ' and ' (b ) ' if and only if ( u ) and ( v ) vectors are not parallel means none of ( u ) and ( v ) is a scalar multiple of the other. Hence, option (b) correct.