Q: Given two vectors $$\\vec{A}$$ and $$\\vec{B}$$, which operation results in a scalar quantity?

Dot product: $$\\vec{A} \\cdot \\vec{B}$$

Q: A vector is represented on a grid as an arrow from $$(2, 3) to$$ $$(5, 7). $$What is the magnitude of this vector?

$$\\sqrt{(5-2)^2$ + (7-3)^2$} = \\sqrt{9 + 16} = \\sqrt{25} = 5$$

Q: A vector $$\\vec{V} is $$described as $$\\vec{V} = 4\\hat{i} + 3\\hat{j}. $$What is the direction of $$\\vec{V}$$ with respect to the positive x-axis?

$$\\tan$$^{-1}$$\\left(\\frac{3}{4}\\right)$$

Q: A pilot flies 100 km north, then 100 km east. What is the magnitude of the displacement vector?

$$\\sqrt{100^2$ + 100^2$} = \\sqrt{20000} = 141.42 km$$

Q: If $$\\vec{A}$$ and $$\\vec{B}$$ are parallel and point in the same direction, what is $$\\vec{A} \\cdot \\vec{B}$$?

$$|\\vec{A}| \\cdot |\\vec{B}|$$

Q: A vector $$\\vec{C}$$ has components $$\\vec{C} = -6\\hat{i} + 8\\hat{j}. $$What is its magnitude?

$$\\sqrt{(-6)^2$ + 8^2$} = \\sqrt{36 + 64} = \\sqrt{100} = 10$$

Q: A car travels 60 km east and then 80 km north. What is the direction of the displacement vector from the starting point?

$$\\tan$$^{-1}$$\\left(\\frac{80}{60}\\right)$$ north of east

Question 1

Which of the following statements is true about vectors in trigonometry?

Accepted Answer

A vector has both magnitude and direction.

Question 2

Given two vectors $$\vec{A}$$ and $$\vec{B}$$, which operation results in a scalar quantity?

Accepted Answer

Dot product: $$\vec{A} \cdot \vec{B}$$

Question 3

If two vectors point in the same direction, what is the angle $$\theta$$ between them?

Accepted Answer

$$\theta = 0^\circ$$

Question 4

A vector is represented on a grid as an arrow from $$(2, 3) to$$ $$(5, 7). $$What is the magnitude of this vector?

Accepted Answer

$$\sqrt{(5-2)^2$ + (7-3)^2$} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Question 5

Which of the following is NOT a property of vectors?

Accepted Answer

Vectors can be divided by another vector.

Question 6

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is the value of their dot product?

Accepted Answer

$$0$$

Question 7

Which statement best describes a scalar quantity?

Accepted Answer

A scalar has only magnitude.

Question 8

A vector $$\vec{V} is $$described as $$\vec{V} = 4\hat{i} + 3\hat{j}. $$What is the direction of $$\vec{V}$$ with respect to the positive x-axis?

Accepted Answer

$$\tan$$^{-1}$$\left(\frac{3}{4}\right)$$

Question 9

Which of the following is a real-world example of a vector quantity?

Accepted Answer

Displacement

Question 10

If $$\vec{A} = 2\hat{i} + 5\hat{j}$$ and $$\vec{B} = 3\hat{i} - 2\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$5\hat{i} + 3\hat{j}$$

Question 11

A pilot flies 100 km north, then 100 km east. What is the magnitude of the displacement vector?

Accepted Answer

$$\sqrt{100^2$ + 100^2$} = \sqrt{20000} = 141.42 km$$

Question 12

Which of the following statements is true regarding the sum of two vectors?

Accepted Answer

The sum of two vectors is a vector.

Question 13

If $$\vec{A}$$ and $$\vec{B}$$ are parallel and point in the same direction, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$|\vec{A}| \cdot |\vec{B}|$$

Question 14

Which of the following is NOT a vector quantity?

Accepted Answer

Distance

Question 15

A vector $$\vec{C}$$ has components $$\vec{C} = -6\hat{i} + 8\hat{j}. $$What is its magnitude?

Accepted Answer

$$\sqrt{(-6)^2$ + 8^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 16

Which operation is used to find the projection of one vector onto another?

Accepted Answer

Dot product

Question 17

If $$\vec{D} is a $$vector with magnitude $$7$$ and points in the negative y-direction, which of the following represents $$\vec{D}$$?

Accepted Answer

$$-7\hat{j}$$

Question 18

A car travels 60 km east and then 80 km north. What is the direction of the displacement vector from the starting point?

Accepted Answer

$$\tan$$^{-1}$$\left(\frac{80}{60}\right)$$ north of east

Vectors and Their Properties: True/False Questions

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