# How do you change the magnitude of a vector?

#### omicron

Three vectors a, b and c are such that a = i + 3j, b = 2i + j and c = i + 13j. Find
(i) the vector which is parallel to a + b and of magnitude 20 units.
(ii) the value of p and of q for which pa + qb = c

I need help in both parts.

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#### mattmns

i)

what is a+b ?

Then, what is the definition of a unit vector? And then how do you change the magnitude of a vector?

ii) What does pa mean, and qb mean? You will have two equations. One will solve the c i component, the other will solve the c j component.

#### Chris Danger

what is the magnitude of a + b?
you need a vector of maginutude 20, in the same direction of a + b.
the scale of your magnitudes should be the same as the scale of your components. (check it for yourself - can you see it's just similar triangles?)

look out for this nice 3,4,5 triangle; they can simplify calculations if you spot them.
i.e where two sides are of length 3 and 4 units, while the hypotenuse is 5 units. that is, if you have a triangle with two of the sides being any two of these numbers, you know immediately the other side must be the missing number.
5,12,13 is another one to look out for. a bit trickier to spot.
These pop up frequently!

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Thank you.

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