Q: What is the direction angle $$\theta of $$the vector $$\vec{u} = (4, 3)$$ measured counterclockwise from the positive x-axis?

$$\theta = \arctan\left(\frac{3}{4}\right)$$

Question 1

Given vectors $$\vec{a} = (4, 3)$$ and $$\vec{b} = (2, -1)$$, what is the magnitude of the vector $$\vec{a} - \vec{b}$$?

Accepted Answer

$$\sqrt{29}$$

Question 2

If $$\vec{u} = (4, 3)$$ and $$\vec{v} = (2, -1)$$, which of the following represents $$\vec{u} + \vec{v}$$?

Accepted Answer

$$(6, 2)$$

Question 3

What is the direction angle $$	heta of $$the vector $$\vec{u} = (4, 3)$$ measured counterclockwise from the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{3}{4}ight)$$

Question 4

A plane travels in the direction of the vector $$\vec{v} = (2, -1). If $$the wind adds a velocity of $$\vec{w} = (1, 2)$$, what is the resultant velocity vector?

Accepted Answer

$$(3, 1)$$

Question 5

Which of the following is the correct formula for the magnitude of a vector $$\vec{a} = (x, y)$$?

Accepted Answer

$$\sqrt{x^2$ + y^2$}$$

Question 6

If $$\vec{a} = (4, 3)$$, what is the unit vector in the direction of $$\vec{a}$$?

Accepted Answer

$$\left(\frac{4}{5}, \frac{3}{5}\right)$$

Question 7

A force of $$\vec{F} = (4, 3) N is $$applied to an object. What is the work done if the object moves $$5$$ meters in the direction of $$\vec{F}$$?

Accepted Answer

$$25 J$$

Question 8

Which vector is perpendicular to $$\vec{u} = (4, 3)$$?

Accepted Answer

$$(3, -4)$$

Question 9

If $$\vec{a} = (4, 3)$$ and $$\vec{b} = (2, -1)$$, what is the dot product $$\vec{a} \cdot \vec{b}$$?

Accepted Answer

Question 10

A boat is moving with velocity $$\vec{v} = (4, 3) km/h. If $$the current flows with velocity $$\vec{c} = (-2, 1) km/h$$, what is the boat's actual velocity?

Accepted Answer

$$(2, 4) km/h$$

Introduction to Geometric Vectors

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