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TS EAMCET 9-Sep-2020 Shift 1 Solved Paper

Section: Mathematics
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Question : 33 of 160
Marks: +1, -0
If a−,b−, and c−\overset{-}{a}, \overset{-}{b}, \text{ and } \overset{-}{c} be three non-coplanar vectors and p−,q− and r−\overset{-}{p}, \overset{-}{q} \text{ and } \overset{-}{r} be defined by
p−=b−×c−a−.(b−×c−)\overset{-}{p} = \frac{\overset{-}{b} \times \overset{-}{c}}{\overset{-}{a}.\left(\overset{-}{b} \times \overset{-}{c}\right)}, q−=c−×a−b−.(c−×a−)\overset{-}{q} = \frac{\overset{-}{c} \times \overset{-}{a}}{\overset{-}{b}.\left(\overset{-}{c} \times \overset{-}{a}\right)}, r−=a−×b−c−.(a−×b−)\overset{-}{r} = \frac{\overset{-}{a} \times \overset{-}{b}}{\overset{-}{c}.\left(\overset{-}{a} \times \overset{-}{b}\right)} such that
α=(a−+b−).p−+(b−+c−).q−+(c−+a−).r−\alpha = \left(\overset{-}{a} + \overset{-}{b}\right).\overset{-}{p} + \left(\overset{-}{b} + \overset{-}{c}\right).\overset{-}{q} + \left(\overset{-}{c} + \overset{-}{a}\right).\overset{-}{r} and β=(a−+b−).(b−+c−)×(a−+b−+c−)b−.(a−×c−)\beta = \frac{\left(\overset{-}{a} + \overset{-}{b}\right).\left(\overset{-}{b} + \overset{-}{c}\right) \times \left(\overset{-}{a} + \overset{-}{b} + \overset{-}{c}\right)}{\overset{-}{b}.\left(\overset{-}{a} \times \overset{-}{c}\right)}, the α+β=\alpha + \beta =
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