5. A system of forces F,, E, and F, acting through points with position vectors r,r, and r, respectively, where F, = (31 – 3j + 4k)N, E = (3i + 4j + 3k)N, E (-4i – 2j + Ak)N, 5 = (i +j+ k)m ņ = (3i + 2j + k)m r, = (2i – j)m reduces to a couple Gand a single force F = (2i – j+ 8k)N acting through the point with position vector r, = (2i – j+ 2k) Find (i) the value of A, (ii) the vector moment of F, about the point with position vector r,, (iii) the Cartesian equation of the line of action of F, (iv) the magnitude of the couple G.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Answer i, ii, iii, iv
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