InterviewSolution
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InterviewSolution
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If vector ` vec b=(t a nalpha,-12sqrt(sinalpha//2))a n d vec c=(t a nalpha, t a nalpha-3/(sqrt(sinalpha//2)))`are orthogonal and vector ` vec a=(13,sin2alpha)`makes an obtuse angle withthe z-axis, then the value of `alpha`is`alpha=(4n+1)pi+tan^(-1)2`b. `alpha=(4n+1)pi-tan^(-1)2`c. `alpha=(4n+2)pi+tan^(-1)2`d. `alpha=(4n+2)pi-tan^(-1)2`A. `alpha= ( 4n+1 ) pi + tan^(-1) 2`B. `alpha= ( 4n+1 ) pi - tan^(-1) 2`C. `alpha= ( 4n+2 ) pi + tan^(-1) 2`D. `alpha= ( 4n+2 ) pi - tan^(-1) 2` |
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Answer» Correct Answer - b,d Since `veca = 1,3, sin 2 alpha) ` makes on abtuse angle with the z-axis its z-component is negtive, thus, ` -1 le sin 2 alpha lt 0` But `vecb.vecc=0` ` tan^(2) alpha - tan alpha -6 =0` `(tan alpha -3) (tan alpha + 2) =0` ` Rightarrow tan alpha 3, -2` Now, `tan alpha =3,` therefore, `sin2 alpha = (2 tanalpha)/(1+tan^(2)alpha)= 6/(1+9)= 3/5` ( not possible as `sin 2 alpha lt 0`) Now , if ` tan alpha = -2` `Rightarrow sin2 alpha= (2tan alpha)/(1+ tan^(2)alpha)= (-4)/(1+_5) = (-4)/5` `tan 2 alpha gt0` Hence, ` 2alpha` is the third quadrant , Also , `sqrt(sin alpha//2)` is meaningful. if `0 lt sin alpha//2 1, ` then `alpha= (4 n + 1) pi-tan^(-1)2` `and alpha= (4n+2) pi - tan^(-1) 2` |
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