Use each set of line segments to sketch a triangle. If a triangle cannot be drawn, explain why.

Mathematics

1 answer:

melamori03 [73]3 years ago

8 0

I don't think it can becauze of u count the squares and try 2 plan out the triangle u cant or i should say me i cant see a triangle being formed

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X-3 ----- = -1 how do I solve this? 22

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Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Gi

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Answer:

angle of intersection: 5.2°

Step-by-step explanation:

The direction vector normal to the plane is ...

n = (1, 1, 3)

The direction vector of the line is ...

m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

n•m = |n|·|m|·cos(θ)

(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

1 = 11·cos(θ)

θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.

acute angle = 90° -84.8° = 5.2°

_____

The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.