Which one of the following pair cannot be the rectangular component of force vector of 10 N?
1)6N& 8N
2)7N & root 51N
3)6root2& 2root7
4)9N & 1N
As you know, 10N is the hypotenuse of the right angled triangle. Hence use Pythagorus theorem to check if the LHS=RHS.
i) (6)²+(8)² =36+64= (10)²= 100
ii) (7)² + (√51)² =49 + 51 = 100
iii) (6√2)²+(2√7)² = 36 x 2 + 4 x 7 = 100
However, (9)² + (1)² = 81+1 =82 ≠ 100
Therefore it cannot be a rectangular component of force vector 10N/.
⓸ is the correct answer
i) (6)²+(8)² =36+64= (10)²= 100
ii) (7)² + (√51)² =49 + 51 = 100
iii) (6√2)²+(2√7)² = 36 x 2 + 4 x 7 = 100
However, (9)² + (1)² = 81+1 =82 ≠ 100
Therefore it cannot be a rectangular component of force vector 10N/.
⓸ is the correct answer