Question

The line of action of 100 Newton force F passes through points A (2,5,8)

and B (7,2,6). Direction of force is from A to B. Express F in terms of unit

vectors i, j, and k.

A. (81.11i-48.67j-32.44k)

B. (81.11i+48.67j+32.44k)

C. (48.67i-32.44j+81.11k)

D. (81.11i+48.67j-32.44k)​

Answer 1

Given,

The line of action of 100 Newton force F passes through points A(2,5,8) and B (7,2,6) Direction of force is from A to B.

To express,

Force in terms of unit vector i, j and k.

magnitude of force, |F| = 100 N

direction of force from A to B, r = B(7,2,6) - A(2,5,8)

= (7 - 2)i + (2 - 5)j + (6 - 8)k

= 5i - 3j - 2k

now unit vector of r , r^ = r/|r|

= (5i - 3j - 2k)/|5i - 3j - 2k|

= (5i - 3j - 2k)/√(5² + 3² + 2²)

= (5i - 3j - 2k)/√38

= (5/√38)i - (3/√38)j - (2/√38)k

= 0.8111 i - 0.4866 j - 0.3244 k

now force in terms of unit vectors, F = |F|r^

= 100(0.8111 i - 0.4866 j - 0.3244 k)

= 81.11i - 48.66j - 32.44k

Therefore option (A) 81.11i - 48.66j - 32.44k , is correct choice.