If vector a⃗=20ı^a⃗=20îa⃗=20ı^ and vector b⃗=50ȷ^b⃗=50ĵb⃗=50ȷ^ calculate a⃗−b⃗a ⃗-b ⃗a⃗−b⃗ using ı^îı^ and ȷ^ĵȷ^ notation.

20ı^−50ȷ^20î-50ĵ20ı^−50ȷ^

If vector a ⃗ = 20 ı ^ a⃗=20î a ⃗ = 20 ı ^ and vector b ⃗ = 50 ȷ ^ b⃗=50ĵ b ⃗ = 50 ȷ ^ calculate a ⃗ − b ⃗ a ⃗-b ⃗ a ⃗ − b ⃗ using ı ^ î ı ^ and ȷ ^ ĵ ȷ ^ notation.

Let's give this problem a try. So in this problem we are told if vector a is equal to 20 I, and vector b is equal to 50 j, calculate vector a minus vector b using I and j notation. Now to solve this problem, well, let's write out what we're looking for. We're looking for vector a minus vector b, and we can see that both of these vectors are given to us in the problem. Vector a we can see is 20i, and vector b is 50j. Now we're asked to find a minus b, so I'm going to need to subtract these 2 vectors. Now the question becomes how can we combine things from here? Well, we actually can't really combine anything because recall that when adding or subtracting vectors you have to combine the like components, and I notice here that we have an 'i' and we have a 'j' those are not the same components, and so we can't combine them. So all we're going to end up with for vector a minus vector b is 20i minus 50j. So So this new vector that we form is going to be 20 units to the right horizontally and 50 units down. So this right here would be our vector a minus b, and that is the solution to the problem. So hope you found this video helpful, thanks for watching.

If vector a⃗=20ı^a⃗=20îa⃗=20ı^ and vector b⃗=50ȷ^b⃗=50ĵb⃗=50ȷ^ calculate a⃗−b⃗a ⃗-b ⃗a⃗−b⃗ using ı^îı^ and ȷ^ĵȷ^ notation.

20ı^−50ȷ^20î-50ĵ20ı^−50ȷ^

20ı^+50ȷ^20î+50ĵ20ı^+50ȷ^

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 $a⃗=20î$ and vector $b⃗=50ĵ$ calculate $a ⃗-b ⃗$ using $î$ and $ĵ$ notation.

$-30ĵ$

$20î-50ĵ$

$30î̂$

$20î+50ĵ$

Verified step by step guidance

Identify the given vectors: $ \vec{a} = 20\hat{i} $ and $ \vec{b} = 50\hat{j} $.

Understand that $ \vec{a} - \vec{b} $ involves subtracting the components of $ \vec{b} $ from $ \vec{a} $.

Since $ \vec{a} $ has only an $ \hat{i} $ component and $ \vec{b} $ has only a $ \hat{j} $ component, the subtraction is straightforward: $ 20\hat{i} - 50\hat{j} $.

Write the result of the subtraction in vector notation: $ 20\hat{i} - 50\hat{j} $.

Verify that the subtraction is correct by checking that each component is handled separately: the $ \hat{i} $ component remains 20 and the $ \hat{j} $ component becomes -50.

2:17m

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