TS EAMCET 19-July-2022 Shift 1 Solved Paper

Let Position vector of A=‌

^

i

−‌

^

j

−2‌

^

k

, Position
vector of B is −2‌

^

i

+‌

^

j

−2‌

^

k

, Position vector of C is
−‌

^

i

−2‌

^

j

+‌

^

k

and Position vectorof D is
2‌

^

i

+2‌

^

j

+a‌

^

k

‌AB=−3‌

^

i

+2‌

^

j

‌AC=−2‌

^

i

−‌

^

j

+3‌

^

k

‌AD=‌

^

i

+3‌

^

j

+(a+2)‌

^

k

Volume of tetrahedron =‌

1

6

[ABACAD]
‌

1

6

|

−3	2	0
−2	−1	3
1	3	a+2

|=‌

20

3

‌−3(−a−2−9)−2(2−a−4−3)
‌=−3(−a−11)−2(−2a−7)=40
‌|3a+33+4a+14|=40
‌|7a+47|=40
‌7a+47=40 or 7a+47=−40
‌7a=−7 or 7a=−87⇒a=−1 or a=−‌

87

7

Hence, integral value of a is −1.