Question

Let a, b, c be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then | a+ b+ c| in terms of θ is equal to

• A. (1+cosθ)√(cos 2θ)
• B. (1+cosθ)√(1-2cosθ)
• C. (1-cosθ)√(1+2cosθ)
• D. None of these

Hint:

Use | u+ v|²=| u|²+| v|²+2 u· v.

Answer 1

The Correct Option is D

| a+ b+ c|² =| a|²+| b|²+| c|² +2( a· b+ b· c+ c· a) Since all are unit vectors and mutually inclined at angle θ: | a+ b+ c|²=3+6cosθ | a+ b+ c|=√(3(1+2cosθ)) This does not match any given option.