1. Find an ordered pair that represents 6 vector v - 5 vector w if vector v =(9,5) and vector w = (6,9).
2. Find an ordered triple that represents 6 vector y + 4 vector z if vector y = (2,6,8) and vector z = (7,-2,6)
3. Find the magnitude of vector WX for W(3, –3, 1) and X(8, –3, –6).
4. Vectors A and B have the same direction. Vector A has a magnitude of 8, and Vector B has a magnitude of 5. What must be true about vectors A and B ? (1 point)
They are opposites and parallel.
They are parallel, but not equal.
They are equal, but not parallel.
They are opposites, but not parallel.
5. Vectors A and B have different, but not opposite directions. Vector A has a magnitude of 7 and vector B has a magnitude of 6. What must be true about Vectors A and B? (1 point)
They are not parallel, opposites, or equal.
They are parallel, but not equal.
They are opposites and parallel.
They are parallel, but not opposites.
6v-5w = 6(9,5)-5(6,9) = (54,30)-(30,45) = (24,-15)
do #2 the same way
|WX| = √(5^2+0^2+7^2) = √74
#4: ║ but ≠
#5: ~║ ~opposites ≠
1. To find the ordered pair that represents 6v - 5w, you need to perform scalar multiplication and vector subtraction.
Given v = (9, 5) and w = (6, 9), multiplying each component of v by 6 and each component of w by 5 gives you:
6v = (6 * 9, 6 * 5) = (54, 30)
5w = (5 * 6, 5 * 9) = (30, 45)
Now, subtracting each component of 5w from 6v gives you:
6v - 5w = (54 - 30, 30 - 45) = (24, -15)
Therefore, the ordered pair representing 6v - 5w is (24, -15).
2. To find the ordered triple that represents 6y + 4z, you need to perform scalar multiplication and vector addition.
Given y = (2, 6, 8) and z = (7, -2, 6), multiplying each component of y by 6 and each component of z by 4 gives you:
6y = (6 * 2, 6 * 6, 6 * 8) = (12, 36, 48)
4z = (4 * 7, 4 * (-2), 4 * 6) = (28, -8, 24)
Now, adding each component of 6y to 4z gives you:
6y + 4z = (12 + 28, 36 + (-8), 48 + 24) = (40, 28, 72)
Therefore, the ordered triple representing 6y + 4z is (40, 28, 72).
3. To find the magnitude of vector WX, you can use the formula for the magnitude of a vector:
The magnitude of WX is given by the formula ||WX|| = √(x^2 + y^2 + z^2), where (x, y, z) are the components of vector WX.
Given W(3, -3, 1) and X(8, -3, -6), the components of vector WX are (8 - 3, -3 - (-3), -6 - 1) = (5, 0, -7).
Plugging these values into the magnitude formula:
||WX|| = √(5^2 + 0^2 + (-7)^2) = √(25 + 0 + 49) = √74
Therefore, the magnitude of vector WX is √74.
4. Vector A and vector B have the same direction if they are parallel. If vector A has a magnitude of 8 and vector B has a magnitude of 5, for them to be in the same direction but not equal, vector A must be a scalar multiple of vector B.
Since the magnitudes are different, vectors A and B cannot be equal.
However, for them to be in the same direction, vector A must be a scalar multiple of vector B.
Therefore, the correct statement is: They are parallel, but not equal.
5. Vector A and vector B have different, but not opposite directions if they are not parallel and not in the same line. If vector A has a magnitude of 7 and vector B has a magnitude of 6, they can have different directions and still not be parallel or equal.
Since the magnitudes are different and they are not opposite, vectors A and B cannot be equal or in the same line.
However, they can have different directions without being parallel.
Therefore, the correct statement is: They are not parallel, opposites, or equal.