Question

Two vectors $\vec{a}$ and $\vec{b}$, add up to vector $\vec{c}$. When vector $\vec{a}$ is made $3$ times as long and vector $\vec{b}$ is doubled in length, without changing their directions, then it is found that vector $\vec{c}$ is also doubled in length, without change in direction. Then which of the following is true?

• A. All three vectors must be parallel
• B. $\vec{b}$ and $\vec{c}$ must be parallel to each other, but $\vec{a}$ need not be parallel to $\vec{b}$ and $\vec{c}$
• C. $\vec{a}$ and $\vec{b}$ must be perpendicular to each other
• D. It is impossible for three non-zero vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ to have the property stated above

Answer 1

Answer: (D)

It is impossible for three non-zero vectors $a, b$ and $c$ to have the property stated above