Two vectors X and Y have equal magnitude. The magnitude of (X - Y) is n times the magnitude of (X + Y). The angle between X and Y is :
Two vectors X and Y have equal magnitude. The magnitude of (X - Y) is n times the magnitude of (X + Y). The angle between X and Y is :
Option 1 -
cos⁻¹((n² + 1)/(n² - 1))
Option 2 -
cos⁻¹((n² - 1)/(-n² - 1))
Option 3 -
cos⁻¹((n² - 1)/(-n² - 1))
Option 4 -
cos⁻¹((n² + 1)/(-n² - 1))
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:According to question
|x| = |y| and
|x - y| = n|x + y|
x² + y² - 2x·y = n² (x² + y² + 2x·y)
(1 - n²) (x² + y²) = (1 + n²)2x·y
(1 - n²) (x² + y²) = (1 + n²)2xy cosθ
(1 - n²) (2x²) = (1 + n²) (2x²)cosθ
cos θ = (1 - n²)/ (1 + n²)
θ = cos? ¹ (1 - n²)/ (1 + n²) = cos? ¹ (- (n²-1)/ (n²+1)
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