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

Lesson 6: Unit vectors

# Worked example: Scaling unit vectors

Watch Sal scale up a unit vector to have a magnitude greater than 1. Created by Sal Khan.

## Want to join the conversation?

• How do you scale up a vector?
• You multiply your equation by a number, like in the video.
For example, if vector U coordinates are (3, 7) and if you want to scale it by two, then you multiply the coordinates by two. Like, 3*2 and 7*2, then your new coordinates of your vector would be, (6, 14).
• previously Sal explained two unit vectors- i^ and j^. How are these unit vectors different from them??
• The unit vectors i and j usually refer to the specific unit vectors <1, 0> and <0, 1>, which are oriented horizontally and vertically and each have magnitude 1.
The unit vectors that we find here could have different directions (since the problems often ask us to find a unit vector in the same direction as another vector), but they have to have magnitudes of 1. The main difference between these and i or j is just the direction that they point in.
• Is it possible to scale with negative numbers?
• Yes, a negative number reverses the direction and scales; so -1 would just reverse the direction, -5 would reverse and increase the vector 5 times in magnitude, etc. . .
• What is the need to introduce this concept of unit vector?
• Suppose, a question asks us to find a vector with some magnitude, say 3, and the direction same as that of a vector, say 2i+3j+3k. Now, since given vector has a direction, which we have to consider, along with a magnitude, which we do not have to consider. Thus to get rid off that magnitude, so that we could simply multiply the given magnitude with the unit vector of the given vector, we use unit vectors.
• at 0.17 Mr Sal Khan used pythagoras theorem to find the magnitude of the vector but in some previous videos he added both horizontal and vertical components. Should we use pythagoras theorem or add both the vectors. I am confused .
(1 vote)
• Vectors have both a magnitude and a direction. Adding hor and ver will give you the direction of the resulting vector, but the Pythagorean thm will give you the magnitude of the result.
• can we multiply vectors by vectors ?
• Is it possible to scale up the 'x' and 'y' components by different factors?
• This would end up changing the direction of the vector. Usually, when we scale a vector, we wish to preserve its direction and only change its magnitude. Otherwise, there's really no significant relationship between the original vector and the "scaled" one.
(1 vote)
• Is it a convention to write i first instead of j?
(1 vote)
• No, it's not a convention. Unit vector I is defined as a shift of 1 in the horizontal direction (1 to the right). Unit vector j is defined as a shift of 1 in the vertical direction (1 up). Since vectors are defined as ( shift in x, shift in y) the i must come first.