Solve the system of equations,
1 answer:
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Answer:
a and b are perpendicular to each other, as are b and d, b and g
Step-by-step explanation:
To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.
We can find the angle between to vectors a and b from the following relation:
The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.
So
cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.
Now, for your exercise, let's compute the dot product between these vectors.
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a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0
So a and b are perpendicular to each other.
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a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5
a and c are not perpendicular to each other.
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a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7
So not perpendicular
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a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11
Not
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b.c = (1,1,4).(1,3,1) = 1+3+4 = 8
Not
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b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0
b.d = 0, so b and d are perpendicular to each other
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b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0
b.g = 0, perpendicular
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c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9
No
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c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5
No
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d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7
No
Check the pictures below.
make sure your calculator is in Degree mode, since the angles are in degrees.
make sure your calculator is in Degree mode, since the angles are in degrees.