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### Course: Algebra (all content)>Unit 19

Lesson 5: Combined vector operations

# Combined vector operations

Watch Sal find new vector 3u + 1/5w when u = (2, -1) and w = (-5, 5).

## Want to join the conversation?

• My answer includes a square root. How do I indicate a square root using characters from the keyboard?
• You can just type in "sqrt" in the answer box and you should get a square root. Alternatively, if you hover the mouse above the answer box you should get several symbols below, one of which is the square root. Click on it.
• Can you add scalars to vectors? Can you multiply vectors by other vectors?
• You cannot add scalar and vector, even if they have the same units (e.g. distance and displacement). Vector multiplication can be done in two ways : Dot product or Cross product.
• if A=[1,4,3] and B=[2,-1,5] then the midpoint M of vector AB..........?
• the midpoint is (1.5,1.5,4)
you just add the co-ordinates in each of the axis and then divide by two. like (1+2)/2,(4+-1)/2,(3+5)/2
• How do we add vectors on graph paper example
• there are previous videos in this section that refer to graphically adding vectors. we can add them by making a triangle. When we add these two vectors we get a resultant vector which is the answer.
• Lets say that vector w is (3,5). so would vector w+1 be (4,6)?
• Can vectors be divided ?
• A vector can be divided by a scalar but a vector cannot be divided by another
However magnitude of vectors can be divided
• how do I find the Magnitude?
(1 vote)
• To find the magnitude of a vector ai+bj, you can use Pythagorean Theorem. The magnitude would be the square root of (a^2+b^2).
Hope this helps! If you have any further questions, please ask! :)
• PLS! I need the same exercise but between 3u and 1/5w we have multiplication!
(1 vote)
• There are two kinds of vector multiplication. I would look in the section that discusses either dot product multiplication (produces a scalar answer) or cross product multiplication (produces a vector orthogonal to the original two input vectors). This is just a beginners intro to vector math.
(1 vote)
• where did the 3 come from or was it apart of the original problem?
(1 vote)
• The 3 is just part of the problem.

We have the vectors 𝒖 and 𝒗,
and we want to find the vector 3𝒖 + (1∕5)𝒗.
(1 vote)
• What about when the vectors are being subtracted?
(1 vote)