GATE EC 2017 Set 2 — Question 3
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Engineering Mathematics → Linear Algebra → Vectors & Vector Operations
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Question
The smaller angle (in degrees) between the planes and is ______.
Correct answer
54 to 55
Solution
The angle between two planes and is the angle between their normal vectors and .For the given planes:
Plane 1:
Plane 2: The cosine of the angle is given by:
Plane 1:
Plane 2: The cosine of the angle is given by:
1.Calculate the dot product:
2.Calculate the magnitudes:
3.Substitute the values into the formula:
4.Find the angle :
The smaller angle is approximately , which falls within the range of 54.0 to 55.0.Continue learning with Success Tracker
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