How do you find the component form AND the magnitude of the vector v with initial point (1, 11) and terminal point (9, 3)?
the resultant vector is
(9-1 , 3-11) = (8,-8)
This is generally considered in component form
check with your textbook how they write the vector.
Some authors avoid the standard round brackets ( ..., ...) to avoid confusion with a point.
Some use this form [8,-8] others use <8 , -8> or some other variation.
the magnitude is √(8^2 + (-8)^2) = √128
= 8√2
To find the component form of a vector, you need to subtract the coordinates of the initial point from the coordinates of the terminal point. Let's call the initial point (x1, y1) and the terminal point (x2, y2).
In this case, the initial point is (1, 11) and the terminal point is (9, 3). So:
x1 = 1, y1 = 11
x2 = 9, y2 = 3
To find the component form of the vector v, subtract the coordinates:
x = x2 - x1 = 9 - 1 = 8
y = y2 - y1 = 3 - 11 = -8
So the component form of the vector v is (8, -8).
To find the magnitude of a vector, you can use the Pythagorean theorem. The magnitude represents the length of the vector.
For vector v with components (x, y), the magnitude is calculated as:
magnitude = sqrt(x^2 + y^2)
In this case, x = 8 and y = -8. Plugging these values into the formula, we get:
magnitude = sqrt(8^2 + (-8)^2)
= sqrt(64 + 64)
= sqrt(128)
= 8√2
So the magnitude of vector v is 8√2 (approximately 11.31).