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 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.

20 ı ^ − 50 ȷ ^ 20î-50ĵ 20 ı ^ − 50 ȷ ^

20 ı ^ + 50 ȷ ^ 20î+50ĵ 20 ı ^ + 50 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 $a⃗=20î$ 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} $ means subtracting the components of $ \vec{b} $ from $ \vec{a} $.

Since $ \vec{a} = 20\hat{i} $ has no $ \hat{j} $ component, its $ \hat{j} $ component is 0. Similarly, $ \vec{b} = 50\hat{j} $ has no $ \hat{i} $ component, so its $ \hat{i} $ component is 0.

Subtract the components: $ (20\hat{i} + 0\hat{j}) - (0\hat{i} + 50\hat{j}) = (20 - 0)\hat{i} + (0 - 50)\hat{j} $.

Simplify the expression to get the result: $ 20\hat{i} - 50\hat{j} $.