### Section 10-2: Two Dimensional Vector Practice

Hey kids in this lesson we reviewed our vectors. We learned a bunch of new vocab which I will give you further down. Hope you don't find this too frustrating. Also, I couldn't figure out how to get the arrows above the letters, so if you think there should be an arrow above it, it's because there should be.

Vector Definitions and Properties

__Vector Quantity__- has both magnitude and direction (eg. - force, velocity, displacement)

__Scalar__- quantity but no direction (eg. - weight, height)

__Vector__- directed line segment that represents a vector quantity (v w/ an arrow above it)

__Tail__- where the vector begins

__Head__- where the vector ends

__Magnitude__- (absolute value is used) the length of a vector

absolute value(v), If v = xi = xj, Then absolute value(v) = square root (x² + y²)

__Unit__

__Vector__- absolute value(u) in the direction of v is a vector that is one unit long in the same direction as v. So u = v/abs(v)* - divide the vector by it's length

Vectors are equal if they have the same magnitude and direction.

The opposite of a vector is the same length in the opposite direction (-v)

__Position Vector__- v = xi + yj; Starts at the origin and the end point is (x,y)

When adding two vectors the resultant vector falls from the tail of the 1st vector to the tip of the 2nd. (Start of the 1st to the end of the 2nd)

* abs() = absolute value

__Example Problem 1__

If a = 4i + 8j and b = 5i - 3j

Find a+b => Add the two equations => 9i -5j

Find a-b => Subtract the two equations=> -i + 11j

Find -a => -4i - 8j

Find 2a + 4b => First multiply a by 5 and b by 4 => 8i +16j and 20i - 12 j => then add => 28i +4j

When doing problems like this make sure you understand that the abs(a) + abs(b) does NOT equal the abs(a + b)

Also, when finding the angle for the vector, use the inverse tangent.

__Example Problem 2__

Given point A (5, 10) and B (8, 20)

Find vector AB (Pointing from A to B)

to do this, look at the given points and subtract. AB = 3i - 10j

Find the position vector of the point 3/4 of the way from A to B.

To do this, it is easier to draw the postion vector to point A, then determine what is 3/4 of AB. Once that is found, add the two vectors.

A = 5i + 10j; 3/4 AB = 3/4(3i - 10j) = (9/4)i - (30/4)j

The answer would then be 5i+10j + (9/4)i - (30/4)j

This equals => 7.25i + 2.5j

Now in honor of March Madness, and USC beating Texas, here is a picture of the Trojan basketball team.

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