If vectors v ⃗ = ⟨ 4 , 3 ⟩ v ⃗=⟨4,3⟩ v ⃗ = ⟨ 4 , 3 ⟩ and u ⃗ = ⟨ 9 , 1 ⟩ u ⃗=⟨9,1⟩ u ⃗ = ⟨ 9 , 1 ⟩ , calculate v ⃗ ⋅ u ⃗ v ⃗⋅u ⃗ v ⃗ ⋅ u ⃗ .

try solving this problem. So here we're told if vector v is equal to 43 and vector u is equal to 91, we're asked to calculate the dot product of v and u. Okay. Now to solve this problem, it's best to be familiar with how to do dot products whether we're dealing with bracket notation or the notation. And here we have the brackets, so what we can do is just recognize that v dot u is going to be this vector 43, and 4 comma 3 is going to be dotted with vector u, which is 9 comma 1. So what I can do is do the typical dot product where we multiply the corresponding components, we multiply 4 and 9, and we multiply the 3 and the 1, and then add the results together. So if we multiply the x components, 49, 9 times 4 is 36, and then we can add this to the product of the y components, which is 3 times 1 or just 3. So we're gonna have 36 plus 3, which is 39. So that right there is the dot product and the solution to this problem. So hope you found this video helpful. Thanks for watching.

If vectors v ⃗ = ⟨ 4 , 3 ⟩ v ⃗=⟨4,3⟩ v ⃗ = ⟨ 4 , 3 ⟩ and u ⃗ = ⟨ 9 , 1 ⟩ u ⃗=⟨9,1⟩ u ⃗ = ⟨ 9 , 1 ⟩ , calculate v ⃗ ⋅ u ⃗ v ⃗⋅u ⃗ v ⃗ ⋅ u ⃗ .

⟨ 36 , 3 ⟩ \langle36,3\rangle ⟨ 36 , 3 ⟩

⟨ 4 , 27 ⟩ \langle4,27\rangle ⟨ 4 , 27 ⟩

8. Vectors

Dot Product

Trigonometry

8. Vectors

Dot Product

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Multiple Choice

If vectors $v ⃗=⟨4,3⟩$ and $u ⃗=⟨9,1⟩$ , calculate $v ⃗⋅u ⃗$ .

$39$

$\langle36,3\rangle$

$33$

$\langle4,27\rangle$

Verified step by step guidance

Understand that the dot product of two vectors $ \mathbf{v} = \langle v_1, v_2 \rangle $ and $ \mathbf{u} = \langle u_1, u_2 \rangle $ is calculated as $ \mathbf{v} \cdot \mathbf{u} = v_1 \cdot u_1 + v_2 \cdot u_2 $.

Identify the components of vector $ \mathbf{v} = \langle 4, 3 \rangle $, where $ v_1 = 4 $ and $ v_2 = 3 $.

Identify the components of vector $ \mathbf{u} = \langle 9, 1 \rangle $, where $ u_1 = 9 $ and $ u_2 = 1 $.

Substitute the components into the dot product formula: $ \mathbf{v} \cdot \mathbf{u} = 4 \cdot 9 + 3 \cdot 1 $.

Calculate each term separately: $ 4 \cdot 9 $ and $ 3 \cdot 1 $, then add the results to find the dot product.

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Struggling with Trigonometry?

If vectors v⃗=⟨4,3⟩v ⃗=⟨4,3⟩v⃗=⟨4,3⟩ and u⃗=⟨9,1⟩u ⃗=⟨9,1⟩u⃗=⟨9,1⟩, calculate v⃗⋅u⃗v ⃗⋅u ⃗v⃗⋅u⃗.

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Dot Product practice set

If vectors $v ⃗=⟨4,3⟩$ and $u ⃗=⟨9,1⟩$ , calculate $v ⃗⋅u ⃗$ .