Indian Navy INET Vectors — practice questions

Explore 2 free Vectors questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Vectors questions and exercises with answers

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Two non-zero vectors $\vec a$ and $\vec b$ are **collinear** (parallel) if and only if there exists a non-zero scalar $m$ such that:Read the answer and worked solution →The position vector of the centroid of the **tetrahedron** with vertices $A(\vec a), B(\vec b), C(\vec c), D(\vec d)$ is:Read the answer and worked solution →

Worked practice questions

Two non-zero vectors $\vec a$ and $\vec b$ are collinear (parallel) if and only if there exists a non-zero scalar $m$ such that:

$\vec a + \vec b = 0$
$\vec a = m\vec b$
$|\vec a| = |\vec b|$
$\vec a \cdot \vec b = 0$

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Correct answer: B. $\vec a = m\vec b$

Collinearity ⇔ one is a scalar multiple of the other: $\vec a = m\vec b$ for some $m \ne 0$. Magnitude equality alone doesn't imply collinearity, and the dot-product condition gives perpendicularity, not parallelism.

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The position vector of the centroid of the tetrahedron with vertices $A(\vec a), B(\vec b), C(\vec c), D(\vec d)$ is:

$(\vec a + \vec b + \vec c)/3$
$(\vec a + \vec b + \vec c + \vec d)/4$
$(\vec a + \vec b + \vec c + \vec d)/3$
$(\vec a \cdot \vec b \cdot \vec c \cdot \vec d)$

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Correct answer: B. $(\vec a + \vec b + \vec c + \vec d)/4$

For a tetrahedron, the centroid divides the line from any vertex to the centroid of the opposite face in ratio 3:1, yielding $\vec g = (\vec a + \vec b + \vec c + \vec d)/4$.

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Indian Navy INET Vectors — practice questions

Vectors questions and exercises with answers

Worked practice questions

Two non-zero vectors $\vec a$ and $\vec b$ are **collinear** (parallel) if and only if there exists a non-zero scalar $m$ such that:

The position vector of the centroid of the **tetrahedron** with vertices $A(\vec a), B(\vec b), C(\vec c), D(\vec d)$ is:

How to practise

More Mathematics topics

Two non-zero vectors $\vec a$ and $\vec b$ are collinear (parallel) if and only if there exists a non-zero scalar $m$ such that:

The position vector of the centroid of the tetrahedron with vertices $A(\vec a), B(\vec b), C(\vec c), D(\vec d)$ is: