If vector v⃗=v ⃗=v⃗= 11ȷ^11ĵ11ȷ^ and vector u⃗=u⃗=u⃗= 10ı^−25ȷ^10î-25ĵ10ı^−25ȷ^ calculate v⃗+15u⃗v⃗+\frac15u⃗v⃗+51u⃗ using ı^îı^ & ȷ^ĵȷ^ notation.

2 ı ^ + 6 ȷ ^ 2î+6ĵ 2 ı ^ + 6 ȷ ^

If vector v ⃗ = v ⃗= v ⃗ = 11 ȷ ^ 11ĵ 11 ȷ ^ and vector u ⃗ = u⃗= u ⃗ = 10 ı ^ − 25 ȷ ^ 10î-25ĵ 10 ı ^ − 25 ȷ ^ calculate v ⃗ + 1 5 u ⃗ v⃗+\frac15u⃗ v ⃗ + 5 1 u ⃗ using ı ^ î ı ^ & ȷ ^ ĵ ȷ ^ notation.

Let's give this problem a try. So in this problem we are told that vector v is equal to 11j, and vector u is equal to 10i minus 25j. We're asked to calculate vector v plus 1 fifth of vector u using I and j notation. Okay, So to start this problem what we need to do, or what I'm gonna do here, is I'm going to write out what we have. So we have vector v plus 1 fifth of vector u, which is what we're trying to find, and we have vector v and u given to us in this problem. So what I can do is replace v and u with the vectors that I see up here. So we're going to have vector 'v' which is just 11j that's what's given to us, and that's going to be plus 1 fifth of vector 'u'. Now vector u I can see right here is 10i minus 25j. So this is what happens if I go ahead and replace these vectors with what we're given. Now from here, 11j is just 11j that's not going to change, but I can take this 1 5th and I can scale it into the vector there. So we'll have 1 5th times 10, and 10 divided by 5 is 2. So that means we're going to have 2 I minus, and then we have 25 divided by 5, which is 5j. Now combining these vectors from here might seem a little bit tricky just because we only have a j component and then here we have an I and a j, but recall that when adding or subtracting vectors you want to do these operations to the like components. So since I can see we only have an 11 j, I'm going to focus on the only j we have in here, which is 5 j. We don't even need to worry about this I since there's no other I component. So 2 I is just gonna remain the same, and then we'll have 11 j minus 5 j because that's gonna be plus, but then this is a negative negative 5. So we have 11 j plus negative 5 j and that's going to come out to 6 j. So I have 2 I plus 6 j, and this right here is the vector and the solution to the problem. So hope you found this video helpful. Thanks for watching.

If vector v ⃗ = v ⃗= v ⃗ = 11 ȷ ^ 11ĵ 11 ȷ ^ and vector u ⃗ = u⃗= u ⃗ = 10 ı ^ − 25 ȷ ^ 10î-25ĵ 10 ı ^ − 25 ȷ ^ calculate v ⃗ + 1 5 u ⃗ v⃗+\frac15u⃗ v ⃗ + 5 1 u ⃗ using ı ^ î ı ^ & ȷ ^ ĵ ȷ ^ notation.

2 ı ^ + 6 ȷ ^ 2î+6ĵ 2 ı ^ + 6 ȷ ^

13 ı ^ + 14 ȷ ^ 13î+14ĵ 13 ı ^ + 14 ȷ ^

2 ı ^ + 14 ȷ ^ 2î+14ĵ 2 ı ^ + 14 ȷ ^

13 ı ^ − 5 ȷ ^ 13î-5ĵ 13 ı ^ − 5 ȷ ^

14. Vectors

Unit Vectors and i & j Notation

Precalculus

14. Vectors

Unit Vectors and i & j Notation

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Multiple Choice

If vector $v ⃗=$ $11ĵ$ and vector $u⃗=$ $10î-25ĵ$ calculate $v⃗+\frac15u⃗$ using $î$ & $ĵ$ notation.

$13î+14ĵ$

$2î+14ĵ$

$13î-5ĵ$

$2î+6ĵ$

Verified step by step guidance

Identify the given vectors: $ \mathbf{v} = 11\mathbf{j} $ and $ \mathbf{u} = 10\mathbf{i} - 25\mathbf{j} $.

Calculate $ \frac{1}{5} \mathbf{u} $ by multiplying each component of $ \mathbf{u} $ by $ \frac{1}{5} $. This gives $ \frac{1}{5} \mathbf{u} = \frac{1}{5}(10\mathbf{i} - 25\mathbf{j}) = 2\mathbf{i} - 5\mathbf{j} $.

Add the vectors $ \mathbf{v} $ and $ \frac{1}{5} \mathbf{u} $ together. This means adding their respective components: $ 0\mathbf{i} + 11\mathbf{j} + 2\mathbf{i} - 5\mathbf{j} $.

Combine the $ \mathbf{i} $ components: $ 0\mathbf{i} + 2\mathbf{i} = 2\mathbf{i} $.

Combine the $ \mathbf{j} $ components: $ 11\mathbf{j} - 5\mathbf{j} = 6\mathbf{j} $. The resulting vector is $ 2\mathbf{i} + 6\mathbf{j} $.

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