If vector v⃗=12ı^−2ȷ^v⃗=12î-2ĵv⃗=12ı^−2ȷ^ and vector u⃗=5ı^+20ȷ^u⃗=5î+20ĵu⃗=5ı^+20ȷ^ calculate 2v⃗−2u⃗2v ⃗-2u ⃗2v⃗−2u⃗ using ı^îı^ and ȷ^ĵȷ^ notation.

14ı^−44ȷ^14î-44ĵ14ı^−44ȷ^

If vector v ⃗ = 12 ı ^ − 2 ȷ ^ v⃗=12î-2ĵ v ⃗ = 12 ı ^ − 2 ȷ ^ and vector u ⃗ = 5 ı ^ + 20 ȷ ^ u⃗=5î+20ĵ u ⃗ = 5 ı ^ + 20 ȷ ^ calculate 2 v ⃗ − 2 u ⃗ 2v ⃗-2u ⃗ 2 v ⃗ − 2 u ⃗ using ı ^ î ı ^ and ȷ ^ ĵ ȷ ^ notation.

Let's try solving this problem. So here we're told if vector v is equal to 12i minus 2j, and vector u is equal to 5i plus 20j, calculate vector 2v minus 2u using ij notation. Okay. Now, to start this problem, what I'm going to do is first take a look at what we're trying to find and that's going to be 2v minus 2u. Now realistically, this is just a situation where we need to operate on these vectors, and we can actually do this and consistently keep the I and j notation, because that's going to be the simplest way to do this problem with the fewest amount of steps. So let's go ahead and do this. Now first off, we have 2v and 2v is just going to be 2 times vector v, which is 12i minus 2j. Now what I'm going to do is subtract this from vector 2u, and 2u is simply going to be 2 multiplied by vector u, which is 5i plus 20j. So this is what we end up with. Now what I can do is scale each of the corresponding vectors. So to find 2v, I'm going to take this 2 and multiply it by both components within v. So we're going to have 2 times 12 which is 24i, and we're going to have 2 times negative 2 which is negative 4j. So this is the vector we end up with for 2v, and next we'll find 2u, and to do this I'll take this 2 and I'll distribute it in for each of the components of vector u. So we're going to have this minus 2 times 5 which is 10i plus and we have 2 times 20 which is 40j. So this is what happens when we scale this vector u by 2. Now from here what I need to do is subtract these 2 vectors, and I can do this by subtracting the corresponding components. So we're going to have 24 I minus 10 I. 24 minus 10 is 14 I, so that's what we end up with. And then we're going to have this, and then we have to do this next operation which is 4 j or negative 4 j, I should say, minus 40 j. Well, if you're in debt $$4 meaning you have negative 4, and you have to lose another 40 $$that means you're going to be in debt $44 total. So negative 4 minuteus 40 is negative 44. So we get 14i minus 44j, and this is the vector that we end up with. So that's how you can find 2v minus 2u. This is the result that we get. So hope you found this video helpful. Thanks for watching.

If vector v⃗=12ı^−2ȷ^v⃗=12î-2ĵv⃗=12ı^−2ȷ^ and vector u⃗=5ı^+20ȷ^u⃗=5î+20ĵu⃗=5ı^+20ȷ^ calculate 2v⃗−2u⃗2v ⃗-2u ⃗2v⃗−2u⃗ using ı^îı^ and ȷ^ĵȷ^ notation.

14ı^−44ȷ^14î-44ĵ14ı^−44ȷ^

7ı^−18ȷ^7î-18ĵ7ı^−18ȷ^

14ı^+44ȷ^14î+44ĵ14ı^+44ȷ^

14ı^−36ȷ^14î-36ĵ14ı^−36ȷ^

8. Vectors

Unit Vectors and i & j Notation

Trigonometry

8. Vectors

Unit Vectors and i & j Notation

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Multiple Choice

If vector $v⃗=12î-2ĵ$ and vector $u⃗=5î+20ĵ$ calculate $2v ⃗-2u ⃗$ using $î$ and $ĵ$ notation.

$14î-44ĵ$

$7î-18ĵ$

$14î+44ĵ$

$14î-36ĵ$

Verified step by step guidance

Identify the given vectors: $ \vec{v} = 12\hat{i} - 2\hat{j} $ and $ \vec{u} = 5\hat{i} + 20\hat{j} $.

Calculate $ 2\vec{v} $ by multiplying each component of $ \vec{v} $ by 2: $ 2\vec{v} = 2(12\hat{i} - 2\hat{j}) = 24\hat{i} - 4\hat{j} $.

Calculate $ 2\vec{u} $ by multiplying each component of $ \vec{u} $ by 2: $ 2\vec{u} = 2(5\hat{i} + 20\hat{j}) = 10\hat{i} + 40\hat{j} $.

Subtract $ 2\vec{u} $ from $ 2\vec{v} $: $ 2\vec{v} - 2\vec{u} = (24\hat{i} - 4\hat{j}) - (10\hat{i} + 40\hat{j}) $.

Combine like terms: $ (24\hat{i} - 10\hat{i}) + (-4\hat{j} - 40\hat{j}) = 14\hat{i} - 44\hat{j} $.

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