Use the dot product to determine which of the following vector pairs are orthogonal.
a. v1 = (-5,5) and v2 = (1,1)
b. v1 = (154,169.4) and v2 = (88,64)
obviously (a)
Yeah, I figured it out once I posted it. Sorry for that! But thanks for responding anyways. I misread read the question. You've been a huge help actually explaining these answers. I'm feeling really good about my final! :)
To determine whether two vectors are orthogonal, we need to check if their dot product is equal to zero.
a. v1 = (-5,5) and v2 = (1,1)
To find the dot product, we multiply corresponding components of the two vectors and then add them together:
v1 · v2 = (-5)(1) + (5)(1) = -5 + 5 = 0
Since the dot product is equal to zero, v1 and v2 are orthogonal.
b. v1 = (154,169.4) and v2 = (88,64)
Similarly, we find the dot product:
v1 · v2 = (154)(88) + (169.4)(64) = 13552 + 10861.6 = 24413.6
Since the dot product is not equal to zero, v1 and v2 are not orthogonal.
To determine if two vectors are orthogonal, we need to take their dot product and check if it equals zero. The dot product of two vectors v1 and v2 is calculated by multiplying their corresponding components and summing the results.
a. v1 = (-5,5) and v2 = (1,1):
The dot product of v1 and v2 is:
v1 · v2 = (-5)(1) + (5)(1) = -5 + 5 = 0.
Since the dot product is equal to zero, vectors v1 and v2 are orthogonal.
b. v1 = (154,169.4) and v2 = (88,64):
The dot product of v1 and v2 is:
v1 · v2 = (154)(88) + (169.4)(64).
To calculate the exact result, we multiply the corresponding components and sum the results:
v1 · v2 = 13552 + 10861.6.
After performing the calculations, we get:
v1 · v2 = 24413.6.
Since the dot product is not equal to zero, vectors v1 and v2 are not orthogonal.
Therefore, the vector pair (a) v1 = (-5,5) and v2 = (1,1) is orthogonal, while the vector pair (b) v1 = (154,169.4) and v2 = (88,64) is not orthogonal.