Q on vectors

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Sonal7

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I did the part a, which is easy. You show that the 3 linear equations are inconsistent. I am unable to do part b.
I don't see how the the line and the plane are parallel.
1584880865448.png
 
Well if the line doesn't meet the plane, it must be parallel to it. What else could it be?
 
Sonal7 said:
View attachment 17345
I did the part a, which is easy. You show that the 3 linear equations are inconsistent. I am unable to do part b.
I don't see how the the line and the plane are parallel.
Click to expand...
The direction vector of the line is \(\vec{D}=<1,1,1>\) while the normal of the plane is \(\vec{N}=<1,1,-2>\).
If you note that \(\vec{D}\cdot\vec{N}=0\) that tells you that the line is perpendicular to the plane's normal.
What does that tell us?
 
Dr.Peterson said:
What is the normal vector to the plane?

What is the direction vector of the line?
Click to expand...
Dr.Peterson said:
What is the normal vector to the plane?

What is the direction vector of the line?
Click to expand...
The direction vector is easy to figure out, is (1,1,1).
I forgot about that the equation rn=k. so now I have the normal.
Since direction vector x normal =0, then the the plane and the line are parallel.
Thank you so much!
 
Yes its also parallel! Vectors are so hard to visualise. Thats why there was 1 mark for it. But is nice to do it the other way, it was more of a proof.
 
Sonal7 said:
The direction vector is easy to figure out, is (1,1,1).
I forgot about that the equation rn=k. so now I have the normal.
Since direction vector x normal =0, then the the plane and the line are parallel.
Thank you so much!
Click to expand...
Of course, you meant the dot product, not the cross product.
 
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