What is a vector?
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What is a vector?
A vector is a type of number with both size and direction.
For example, a vector could represent "4 units to the right".
What is the difference between a vector and a scalar?
A vector has a direction, whereas a scalar is just a number with no direction.
True or False?
represents the vector from to .
True.
represents the vector from to .
True or False?
The vector must be drawn starting at and ending at the point .
False.
The vector does not need to be drawn starting at and ending at the point .
The vector can start at any point, as long as it goes 2 to the right and 3 up.
How do you write "3 to the left and 2 up" as a column vector?
"3 to the left and 2 up" can be written as the column vector .
How do you add two column vectors?
To add two column vectors, add together the numbers in the corresponding parts of the vector.
For example, .
True or False?
False.
.
To multiply a vector by a scale, you need to multiply all parts of the vector by the scalar.
.
If you know what the vectors and look like, how could you draw the vector ?
If you know what the vectors and look like, to draw the vector :
Draw the vector
Draw the vector starting at the end of
Draw a vector from the start of to the end of
True or False?
The vector is in the same direction as but it is double the length.
True.
The vector is in the same direction as but it is double the length.
Scalar multiples of a vector change the length of the vector.
What is the geometrical relationship between the vectors and ?
The vectors and have the same length but they are in opposite directions.
What is meant by the modulus (magnitude) of a vector?
The modulus (magnitude) of a vector is its length.
True or False?
The modulus of the vector is .
False.
The modulus of the vector is not .
To find the modulus of a vector, you square the numbers, add them together and them take the positive square root.
The modulus of the vector is .
True or False?
The modulus of the vector is .
False.
The modulus of the vector is not .
You need to square the negative in front of the 3.
The modulus of the vector is .
True or False?
If two vectors are parallel, then they are scalar multiples.
True.
If two vectors are parallel, then they are scalar multiples.
True or False?
True.
This means if you start at A then go to B and then go to C, this is the same vector as starting at A and going to C.
How else could you write the vector ?
The vector can also be written as .
True or False?
False.
The correct equation is .
A and B have position vectors, and .
Write a formula for the position vector of the midpoint of A and B in terms of and .
A and B have position vectors, and .
A formula for the position vector of the midpoint of A and B is .
True or False?
If the point P divides the line AB in the ratio 1 : 3, then .
False.
If the point P divides the line AB in the ratio 1 : 3, then .
P divides the line into 4 equal parts, two points on one side, and 3 parts on the other side.
The correct equation is .
If the vectors and are parallel, what does this tell you at the three points, , and ?
If the vectors and are parallel, then the three points, , and all lie on the same straight line.