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Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i – 6j
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Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i – 6j
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Mathematics
3 years
2021-08-02T20:40:57+00:00
2021-08-02T20:40:57+00:00 1 Answers
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Answers ( )
Answer:
5
Step-by-step explanation:
I’m going to call x, x1 because I want to use x as a variable.
So we have a ray with points (0,0) and (3×1,5) on it. This equation for this ray would be y=5/(3×1)×x.
We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.
We want these two lines’ slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.
So we want to find x1 such that 5/(3×1)=1/3.
Cross multiply: 15=3×1
Divide both sides by 3: 5=x1
We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.
Another way:
If two vectors are perpendicular, then their dot product is 0.
The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).
Let’s simplify:
6x-30.
We want this to be 0.
6x-30=0
Add 30 on both sides:
6x=30
Divide both sides by 6:
x=5