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Question: If **a**, **b**, **c** are three non-coplanar vectors, then the vector equation \(\mathbf{r} = (1 - ...

If a, b, c are three non-coplanar vectors, then the vector equation r=(1−p−q)a+pb+qc\mathbf{r} = (1 - \mathbf{p} - \mathbf{q})\mathbf{a} + p\mathbf{b} + q\mathbf{c} represents a

A

Straight line

B

Plane

C

Plane passing through the origin

D

Sphere

Answer

Plane

Explanation

Solution

If a,b,c\mathbf{a},\mathbf{b},\mathbf{c} are non-coplanar vectors then the vector equation r=(1−p−q)a+pb+qc\mathbf{r} = (1 - p - q)\mathbf{a} + p\mathbf{b} + q\mathbf{c} represents a plane.