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## Algebra (all content)

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

Lesson 9: Adding vectors in magnitude & direction form

# Adding vectors in magnitude & direction form (2 of 2)

Watch Sal finish the problem he started in part 1 by converting the sum back to magnitude and direction form. Created by Sal Khan.

## Want to join the conversation?

• When Sal calculated the magnitude of vector c using the Pythagoras theorem, why didn't he consider the i 'with the hat' and the j ' with the hat '? •  Good question- in this case however, those symbols don't contain values, they're simply notation (known as 'versors') used to indicate direction in a Cartesian coordinate system. In 3-dimensional vectors, 'k hat' will be introduced and used along with 'i hat' and 'j hat' (think 'x' 'y' and 'z' from algebra).
• Would it not have been easier to convert everything to decimal form and round to the nearest thousandth (or tenth) from the beginning? Typing the entire equation in a calculator (like at ) leaves room for error. Especially when most questions I've come across in the practice sessions ask for decimal answers in the tenth anyway. •  Rounding errors accumulate in equations. If everything was converted to nearest thousandth from the start the end result could be off by quite a bit in the end result.

Lets say that two exact decimal numbers are being multiplied together and the answer is to be rounded to the nearest thousandth.

3.253252 * 4.3333333 = 14.0974252248916 rounded to nearest thousandth gives 14.097

Now try rounding the two numbers to the nearest thousandth first.
3.253 *4.333 = 14.095249 rounded to nearest thousandth is 14.095, the two answers don't match. Errors can get even bigger than that when rounding early if there are even more operations being done.
• In an triangle , the sum of any 2 sides needs to be greater than the third as a rule for it to be possible . So how is that in vector addition , the vector from one end to the head of another can end up being their sum ( as is should be greater than ) ? • At the end of the video Sal says that if the two vectors are going the exact same direction, then the tangent you get by adding them is equal to them. Can someone explain that to me? Because if they're going the same direction, wouldn't that mean they're parallel? And either the parallel vectors aren't touching at all, or they just make a line. And you can't make one of those triangle things to add the two vectors with a line. • When Sal added vector 'a' to vector 'b' to get vector 'c', he visualized this by putting the tail of vector 'b' at the head of vector 'a' and then he created vector 'c' by drawing a line between the tail of vector 'a' and the head of vector 'b'. If the vectors were going the same direction then you would do the same thing to visualize: place the tail of one to the head of the other. They then form one long line because they are going the same direction, and because they are going the same direction you can directly add them without squaring each and taking the square root of the sum. So there is no need to make a triangle.
• Why did we put the value of (vector "a" + vector "b") in place of opposite over adjacent when calculating the tan theta? • Is it possible to add two vectors of unequal magnitudes and get answer as zero ?
If YES , Then how.
Thank you • Is the angle between /A and /B the same as the angle between /A+/B? • can't we measure the angle graphically in the picture he drew by moving the tail of one of the vectors to the tip of another one? Is it not possible to find direction like that   