Find the angle between the following two vectors:a⃗ =⟨0,−5⟩𝑎→=⟨0,−5⟩ and b⃗ =⟨1,−4⟩𝑏→=⟨1,−4⟩(Round your answer to the nearest whole degree.)

To find the angle between two vectors, we can use the dot product formula:

a⃗ . b⃗ = ||a⃗|| ||b⃗|| cos θ

Where:

• a⃗ . b⃗ is the dot product of vectors a and b
• ||a⃗|| is the magnitude of vector a
• ||b⃗|| is the magnitude of vector b
• θ is the angle between vectors a and b

First, let's calculate the dot product of vectors a and b:

a⃗ . b⃗ = (0 * 1) + (-5 * -4) = 20

Next, let's calculate the magnitudes of vectors a and b:

||a⃗|| = sqrt((0^2) + (-5^2)) = sqrt(25) = 5 ||b⃗|| = sqrt((1^2) + (-4^2)) = sqrt(17)

Now, we can substitute these values into the dot product formula and solve for θ:

20 = 5 * sqrt(17) * cos θ cos θ = 20 / (5 * sqrt(17)) θ = cos^-1(20 / (5 * sqrt(17)))

Calculating this gives θ ≈ 16.26 degrees. Rounding to the nearest whole degree gives θ ≈ 16 degrees.

To find the angle between two vectors, we can use the dot product formula:

a⃗ . b⃗ = ||a⃗|| ||b⃗|| cos θ

Where:

• a⃗ . b⃗ is the dot product of a⃗ and b⃗
• ||a⃗|| is the magnitude of a⃗
• ||b⃗|| is the magnitude of b⃗
• θ is the angle between a⃗ and b⃗

Step 1: Calculate the dot product (a⃗ . b⃗) a⃗ . b⃗ = (0 * 1) + (-5 * -4) = 20

Step 2: Calculate the magnitude of a⃗ (||a⃗||) ||a⃗|| = sqrt((0^2) + (-5^2)) = sqrt(25) = 5

Step 3: Calculate the magnitude of b⃗ (||b⃗||) ||b⃗|| = sqrt((1^2) + (-4^2)) = sqrt(17)

Step 4: Substitute these values into the dot product formula and solve for θ 20 = 5 * sqrt(17) * cos θ cos θ = 20 / (5 * sqrt(17)) θ = cos^-1(20 / (5 * sqrt(17)))

Use a calculator to find the inverse cosine of the above expression to get the angle in degrees. Round your answer to the nearest whole degree.