InterviewSolution
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InterviewSolution
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The value of x for which the angle between ` veca = 2x^(2) hati + 4x hatj =hatk +hatk and vecb = 7hati -2hatj =x hatk` , is obtuse and the angle between ` vecb` and the z-axis is acute and less than `pi//6`, areA. ` a lt x lt 1//2`B. ` 1//2 lt x lt 15`C. ` x gt 1//2 or x lt 0`D. none of these |
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Answer» Correct Answer - D The angle between `veca and vecb` is obtuse. `veca.vecb lt 0` ` Rightarrow 14x^(2) - 8x +x gt 0 Rightarrow 7x(2x -1) gt 0 Rightarrow 0 lt x lt 1//2 …(1)` The angle between `vecb` and z-axis is acute and less thann `pi//6` . ` ( vecb.veck)/(|vecb||veck|) gt cos "" pi/6 " " [ therefore, theta , pi/6 Rightarrow cos theta gt cos "" pi/6]` ` x/ (sqrt(x^(2) +53)) gt sqrt3/2` ` Rightarrow 4x^(2) gt 3x^(2) + 159` ` Rightarrow x^(2) gt 159 Rightarrow gt sqrt(159) or x gt - sqrt159 ` Clearly, (i) and (ii) cannot hold togerther. |
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