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AP EAMCET Euclidean Vector — practice questions

Explore 48 free Euclidean Vector questions in AP EAMCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Euclidean Vector questions and exercises with answers

Showing questions 1–30 of 48.

Which pair of properties defines a Euclidean vector?Read the answer and worked solution →To add b to a graphically, where is the tail of b placed?Read the answer and worked solution →In the parallelogram rule, a + b is represented by which part of the parallelogram?Read the answer and worked solution →Adding the vectors (1, 2, 3) and (-2, 0, 4) gives which vector?Read the answer and worked solution →A ship's displacements are a = (3, 4) km and b = (1, -2) km. What is the resultant displacement a + b?Read the answer and worked solution →For a = (5, 3) and b = (2, 7), the vector a - b equals which of these?Read the answer and worked solution →Which law does vector addition satisfy, as shown by a + b = b + a?Read the answer and worked solution →How is the sum of three vectors (a + b) + c related to a + (b + c)?Read the answer and worked solution →What is the length of the vector (2, 3, 6)?Read the answer and worked solution →How can a vector of arbitrary length be turned into a unit vector?Read the answer and worked solution →The zero vector is the vector having what length?Read the answer and worked solution →Two vectors are called opposite when they have what relationship?Read the answer and worked solution →Which describes two equidirectional (codirectional) vectors?Read the answer and worked solution →Scalar multiplication distributes over vector addition as which rule?Read the answer and worked solution →Multiplying the vector (2, -1, 3) by the scalar 3 gives which vector?Read the answer and worked solution →The difference a - b can be rewritten using the opposite of b as which sum?Read the answer and worked solution →If a vector has length 5, what is the length of 2a?Read the answer and worked solution →The dot product of two vectors is what kind of quantity?Read the answer and worked solution →The cross product is meaningful only in which dimensions?Read the answer and worked solution →The length of a × b equals the area of which shape?Read the answer and worked solution →The scalar triple product is zero exactly when the three vectors are what?Read the answer and worked solution →A vector with a definite initial point and terminal point is called what?Read the answer and worked solution →A vector whose start and end points do not matter, only size and direction, is called what?Read the answer and worked solution →Who published Elements of Vector Analysis in 1881, essentially the modern system?Read the answer and worked solution →Which mathematician introduced the concept of equipollence in 1835?Read the answer and worked solution →What do we call the vector sum a + b of two vectors?Read the answer and worked solution →The speed of a moving object is which part of its velocity vector?Read the answer and worked solution →Velocity is the time derivative of which vector quantity?Read the answer and worked solution →A hiker walks 3 km east, then 4 km north. What is the magnitude of the net displacement?Read the answer and worked solution →Two forces (2, 1) N and (-5, 3) N act on a body. What is the net force?Read the answer and worked solution →

Worked practice questions

Which pair of properties defines a Euclidean vector?

  1. Mass and weight
  2. Charge and volume
  3. Speed and time
  4. Size and direction
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Correct answer: D. Size and direction

A vector is a geometric object fixed by how long it is and which way it points.

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To add b to a graphically, where is the tail of b placed?

  1. At the tail of a
  2. At the zero point
  3. At the middle of a
  4. At the head of a
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Correct answer: D. At the head of a

In the head-to-tail method, b starts where a ends and the sum runs from the start of a to the end of b.

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In the parallelogram rule, a + b is represented by which part of the parallelogram?

  1. The centre point
  2. A shorter side
  3. The perimeter
  4. A diagonal
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Correct answer: D. A diagonal

The two vectors form adjacent sides and their sum is the diagonal from the common point.

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