Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If $\vec{x}$ and $\vec{y}$ are two collinear vectors, then which of the following are incorrect ?

Options:

$\vec{x}=±\vec{y}$

$\vec{y}=\lambda \vec{x}$, for some scalar $\lambda $

Both the vectors $\vec{x}$ and $\vec{y}$ have same direction, but different magnitudes.

the respective components of $\vec{x}$ and $\vec{y}$ are not proportional

Correct Answer:

Both the vectors $\vec{x}$ and $\vec{y}$ have same direction, but different magnitudes.

Explanation:

The correct answer is Option (3) → Both the vectors $\vec{x}$ and $\vec{y}$ have same direction, but different magnitudes.

for two collinear vectors $\vec x$ and $\vec y$

$\vec x={x_1}\hat i+{x_2}\hat j+{x_3}\hat k$, $\vec y={y_1}\hat i+{y_2}\hat j+{y_3}\hat k$

so $\frac{x_1}{y_1}=\frac{x_2}{y_2}=\frac{x_3}{y_3}$ always