A vector coplanar with the non-collinear vect | vedclass

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Question

(A) vector $\vec{r}$ is coplanar with two non-collinear vectors $\vec{a}$ and $\vec{b}$ if and only if it can be expressed as a linear combination of

Vedclass · Accepted Answer

$x\vec{a} + y\vec{b}$

Vedclass · Answer

(A) vector $\vec{r}$ is coplanar with two non-collinear vectors $\vec{a}$ and $\vec{b}$ if and only if it can be expressed as a linear combination of $\vec{a}$ and $\vec{b}$.That is,$\vec{r} = x\vec{a} + y\vec{b}$ for some scalars $x$ and $y$.Since the provided options do not explicitly include the general form $x\vec{a} + y\vec{b}$ as a standard choice,and option $(B)$ $\vec{a} + \vec{b}$ is a specific case of this linear combination (where $x=1, y=1$),the most appropriate general answer is the linear combination form. However,if the question implies a specific vector from the list,$\vec{a} + \vec{b}$ is indeed coplanar. Given the structure,we select the linear combination form.

$A$ vector coplanar with the non-collinear vectors $\vec{a}$ and $\vec{b}$ is:

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