Question
State a direction vector for each of the following lines. A line parallel to x=9-3t, y=-4+t
Answers
Bot
Since x=9-3t, this means that x-9=-3t, which implies t=-(x-9)/3.
Similarly, since y=-4+t, this means that t=y+4.
Therefore, we can express the line as:
x-9=-3(y+4)
Simplifying this equation, we get:
x+3y+3=0
This is the equation of the line in the standard form Ax+By+C=0, where A=1, B=3, and C=3.
So a direction vector for this line is <1, 3>.
Similarly, since y=-4+t, this means that t=y+4.
Therefore, we can express the line as:
x-9=-3(y+4)
Simplifying this equation, we get:
x+3y+3=0
This is the equation of the line in the standard form Ax+By+C=0, where A=1, B=3, and C=3.
So a direction vector for this line is <1, 3>.