What is a vector?
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What is a vector?
A vector is a type of number with both size and direction.
True or False?
represents the vector from to .
True.
represents the vector from to .
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 .
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 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 scalar, you need to multiply all parts of the vector by the scalar.
.
If you know what the vectors and look like, how can 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 is double the length of .
True.
The vector is in the same direction as but 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 magnitude (modulus) of a vector?
The magnitude (modulus) of a vector is its length.
True or False?
The magnitude of the vector is .
False.
The magnitude of the vector is not .
To find the magnitude of a vector, you square the numbers, add them together and then take the positive square root.
The magnitude of the vector is .
True or False?
The magnitude of the vector is .
False.
The magnitude of the vector is not .
You need to square the negative in front of the 3.
The magnitude of the vector is .
True or False?
False.
The correct equation is .
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?
If two vectors are parallel, then they are scalar multiples.
True.
If two vectors are parallel, then they are scalar multiples.
E.g. the vectors and are parallel.
True or False?
If the point P divides the line AB in the ratio 1Â :Â 3, then .
False.
If the point P divides the line AB in the ratio 1Â :Â 3, then .
P divides the line into 4 equal parts, with 1 part 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 about the three points, , and ?
If the vectors and are parallel, then the three points , and all lie on the same straight line.
Points A and B have position vectors and , respectively.
Write a formula for the position vector of the midpoint of A and B in terms of and .
Points A and B have position vectors and , respectively.
A formula for the position vector of the midpoint of A and B is .