How to Add and Subtract Vectors Step by Step

TL;DR

To add or subtract vectors, combine their corresponding components. For example, adding vectors v = 2i - 5j and w = -3i + 7j yields -i + 2j, while subtracting them gives 5i - 12j. Scalar multiplication also modifies vectors before addition or subtraction, such as 2v + 3w resulting in -5i + 11j.

Transcript

in this lesson we're going to focus on Vector operations we're going to add and subtract vectors so in this problem we have two vectors vector v which is 2i minus 5j and Vector W which is negative 3i Plus 7j so let's perform the indicated operations so let's start with part a let's add V and W so it's 2i minus 5j Plus negative 3i Plus 7j so for thi... Read More

Key Insights

• 🪜 Vector operations involve adding, subtracting, and multiplying vectors by scalar quantities.
• 🪜 Adding vectors involves combining like terms by adding their corresponding components.
• 🤘 Subtracting vectors involves distributing the negative sign and combining like terms.

Questions & Answers

Q: What are the given vectors in the problem?

The given vectors are v = 2i - 5j and w = -3i + 7j.

Q: What is the result of adding v and w?

Adding v and w gives us -i + 2j.

Q: How do we subtract w from v?

To subtract w from v, we distribute the negative sign and combine like terms, resulting in 5i - 12j.

Q: How can we multiply vectors by scalar quantities?

To multiply a vector by a scalar quantity, we multiply each component of the vector by the scalar quantity. In this case, multiplying v by 2 and w by 3 gives us -5i + 11j.

Summary & Key Takeaways

• Two vectors are given: vector v = 2i - 5j and vector w = -3i + 7j.

• Part A: Adding v and w results in -i + 2j.

• Part B: Subtracting w from v gives 5i - 12j.

• Part C: Multiplying v by 2 and w by 3 and adding them gives -5i + 11j.