InterviewSolution
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InterviewSolution
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Suppose that `vec p , vec q and vec r ` non- coplanar vectors in `R^(3)` . Let the components of a vector `vec s " along " vec p , vec q and vec r ` be 4, 3 and 5 respectively. If the components of this vectors `vec s " along " -vec p + vec q + vec r , vec p - vec q + vec r and - vec p - vecq + vec r ` are x , y and z respectively, then the value of `2x-y+z,` isA. 7B. 8C. 9D. 6 |
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Answer» Correct Answer - C It is given that the components of vectors `vecs " along " vecp, vec q and vec r ` are 4, 3 and 5 respectively. `therefore vecs = 4vec p + 3 vecq + 5 vec r " " ` …(i) The components of `vec s ` along `-vec p + vec q + vec r , vec p - vec q + vec r and - vec p - vec q + vec r` and x, y and z respectively. ` therefore vec s = x (- vec p + vec q + vec r ) +y( vec p - vec q + vec r ) + z ( - vec p - vec q + vec r ) ` `rArr vec s = (-x+y-z) vec p + (x-y-z) vec q + (x+y+z) vec r " " ` ...(ii) From (i) and (ii) , we obtain `-x+y-z=4, x-y-z=3 and x+y+z=5` Solving these equations, we obtain `x=4, y=(9)/(2), z=(7)/(2)` `therefore 2x+y+z=8+(9)/(2)-(7)/(2)=9.` |
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