Question 1

Which of the following correctly expresses the position vector $$\vec{r} of an $$object in terms of its $$x$$ and $$y$$ components?

Accepted Answer

$$\vec{r} = x\hat{i} + y\hat{j}$$

Question 2

Given two vectors $$\vec{A} = A_x \hat{i} + A_y \hat{j}$$ and $$\vec{B} = B_x \hat{i} + B_y \hat{j}$$, what is the correct formula for their sum $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\vec{A} + \vec{B} = (A_x + B_x)\hat{i} + (A_y + B_y)\hat{j}$$

Question 3

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and $$\vec{B} = 2\hat{i} + 5\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$5\hat{i} + 9\hat{j}$$

Question 4

Which of the following statements about vectors and scalars is correct?

Accepted Answer

Vectors have both magnitude and direction, while scalars have only magnitude.

Question 5

A car moves 3 meters east and then 4 meters north. What is the magnitude of its displacement vector?

Accepted Answer

$$5$$ meters

Question 6

If $$\vec{r}(t) = x(t)\hat{i} + y(t)\hat{j}$$, what does $$x(t)$$ and $$y(t)$$ represent?

Accepted Answer

The $$x$$ and $$y$$ coordinates of the object's position as functions of time.

Question 7

Which operation is valid for vectors but not for scalars?

Accepted Answer

Vector addition

Question 8

If $$\vec{A} = 5\hat{i} - 2\hat{j}$$ and $$\vec{B} = -3\hat{i} + 6\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$2\hat{i} + 4\hat{j}$$

Question 9

Which of the following is a correct example of a scalar quantity?

Accepted Answer

Temperature

Question 10

A drone flies such that its position at time $$t is $$given by $$\vec{r}(t) = (2t)\hat{i} + (3t^2$)\hat{j}. $$What is the $$y-$$component of its position at $$t = 2 s$$?

Accepted Answer

$$12$$

Question 11

Which of the following best describes the geometric interpretation of vector addition?

Accepted Answer

Placing the tail of the second vector at the head of the first vector and drawing the resultant from the tail of the first to the head of the second.

Question 12

If $$\vec{r} = 4\hat{i} + 3\hat{j}$$, what is the magnitude $$|\vec{r}|$$?

Accepted Answer

$$5$$

Vectors and Position in Physics with Calculus

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