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HPCET Vectors — practice questions

Explore 28 free Vectors questions in HPCET 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

Showing questions 1–28 of 28.

Which of the following is a **vector** quantity?Read the answer and worked solution →The magnitude of the zero (null) vector $\vec 0$ is:Read the answer and worked solution →A unit vector along a non-zero vector $\vec a$ is given by:Read the answer and worked solution →$\overrightarrow{PQ} + \overrightarrow{QR}$ equals (triangle law of addition):Read the answer and worked solution →The magnitude of the vector $\vec a = 4\hat i + 0\hat j + 3\hat k$ is:Read the answer and worked solution →The position vector of the **midpoint** of the segment joining points with position vectors $\vec a$ and $\vec b$ is:Read the answer and worked solution →The triangle inequality for vectors states:Read the answer and worked solution →If $\vec{PQ} = \vec a$, then $\vec{QP}$ equals:Read the answer and worked solution →The position vector of the **centroid** of triangle with vertices $A(\vec a),\ B(\vec b),\ C(\vec c)$ is:Read the answer and worked solution →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 →Vector $\vec a$ is directed due north with $|\vec a| = 24$ and vector $\vec b$ is directed due west with $|\vec b| = 7$. The magnitude $|\vec a + \vec b|$ equals:Read the answer and worked solution →The distance from the point $P(2, 3, 4)$ to the **x-axis** is:Read the answer and worked solution →The point dividing the line segment joining $A(2, -6, 8)$ and $B(-1, 3, -4)$ internally in ratio $1:3$ has coordinates:Read the answer and worked solution →If $\vec a = 4\hat i + 3\hat k$ and $\vec b = -2\hat i + \hat j + 5\hat k$, then $2\vec a + 5\vec b$ equals:Read the answer and worked solution →Vectors $\vec a = \hat i - 2\hat j + 3\hat k$ and $\vec b = 3\hat i - 6\hat j + 9\hat k$ are: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 →If vectors $2\hat i - q\hat j + 3\hat k$ and $4\hat i - 5\hat j + 6\hat k$ are collinear, then $q$ equals:Read the answer and worked solution →Vector $\vec{AB} = 2\hat i - 4\hat j + 7\hat k$ has initial point $A(1, 5, 0)$. The terminal point $B$ has coordinates:Read the answer and worked solution →Find a unit vector in the direction of $\vec a = \hat i - 2\hat j$:Read the answer and worked solution →Find the value of $\lambda$ and $\mu$ if the non-zero, non-collinear vectors $\vec a$ and $\vec b$ satisfy $\vec a + 3\vec b = 2\lambda \vec a - \mu \vec b$:Read the answer and worked solution →Vector $4\hat i + 13\hat j - 18\hat k$ expressed as a linear combination of $\hat i - 2\hat j + 3\hat k$ and $2\hat i + 3\hat j - 4\hat k$ has coefficients $(m, n)$:Read the answer and worked solution →If $\vec a, \vec b, \vec c$ are the position vectors of $A, B, C$ and $5\vec a - 3\vec b - 2\vec c = \vec 0$, then point $C$ divides $\overline{BA}$:Read the answer and worked solution →If $G(a, 2, -1)$ is the centroid of the triangle with vertices $P(1, 3, 2),\ Q(3, b, -4),\ R(5, 1, c)$, then $(a, b, c)$ equals:Read the answer and worked solution →The centroid of the tetrahedron with vertices $A(3, -5, 7),\ B(5, 4, 2),\ C(7, -7, -3),\ D(1, 0, 2)$ is:Read the answer and worked solution →If $A(0, 3, 0), B(0, 0, 4), C(0, 3, 4)$ are vertices of a triangle, the position vector of its **incentre** is:Read the answer and worked solution →Points $A(3, 2, p), B(q, 8, -10), C(-2, -3, 1)$ are collinear. The values of $p$ and $q$ are:Read the answer and worked solution →Match each vector termRead the answer and worked solution →Scalar or vector result?Read the answer and worked solution →

Worked practice questions

Which of the following is a **vector** quantity?

  1. Mass
  2. Temperature
  3. Displacement
  4. Speed
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Correct answer: C. Displacement

A vector needs both magnitude and direction. Displacement has both (e.g. 5 m north). Mass, temperature and speed are completely described by magnitude alone — they are scalars.

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The magnitude of the zero (null) vector $\vec 0$ is:

  1. 1
  2. Undefined
  3. 0
  4. Any positive real number
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Correct answer: C. 0

A zero vector is a vector whose initial and terminal points coincide, so $|\vec 0| = 0$. Its direction can be taken as anything convenient.

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A unit vector along a non-zero vector $\vec a$ is given by:

  1. $\vec a / |\vec a|$
  2. $|\vec a| \cdot \vec a$
  3. $\vec a / 2$
  4. $2\vec a / |\vec a|^2$
Show answer and solution

Correct answer: A. $\vec a / |\vec a|$

$\hat a = \vec a / |\vec a|$ — divide a vector by its magnitude to get a unit vector in the same direction. It always has magnitude 1.

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