Question

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

• A. None of $u$ and $v$ is a scalar multiple of the other.
• B. None of $|u|$ and $|v|$ is a scalar multiple of the other.
• C. $u$ and $v$ have different directions.
• D. $u$ and $v$ are perpendicular to each other.

Answer 1

Answer: (A)

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.