Mathematics, 05.09.2019 21:30, queenskmk1628

Consider the vectors a =3i +j −k, b =i +j +4k, c=i +3j +k, d =−i −3j +k, g =−3i −j +k. which pairs (if any) of these vectors are perpendicular each others?

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answered: thedragontale1020

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 $\theta$ between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.

$cos(\theta) = \frac{a.b}{|a||b|}$

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

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c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5

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d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7

answered: Guest

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

answered: Guest

the answer is 489

step-by-step explanation:

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Consider the vectors a =3i +j −k, b =i +j +4k, c=i +3j +k, d =−i −3j +k, g =−3i −j +k. which pairs (...