Observe the following columns : <table class="MyTable" width="100%"> <tr><th colspan="2" align="center">Column I</t Column I

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Q 2212180939.     Observe the following columns :
Column IColumn II
(A) If `V_1, V_2,V_3` are the volumes of parallelopiped, triangular prism and tetrahedron respectively. The three coterminus edges of all three figures are the vectors ` hat(i) - hat(j) -6 hat(k), hat(i) -hat(j) + 4 hat(k)` and `2 hat(i) -5 hat(j) +3 hat(k)`, then(P) `2V_1 +3 V_3 =5V_2`
(B) If `V_1, V_2,V_3` are the volumes of parallelopiped, triangular prism and tetrahedron respectively. The three coterminus edges of all three figures are the vectors `-2 hat(i) +3 hat(j) - 3 hat(k) , 4 hat(i) + 5hat(j) -3 hat(k)` and `6 hat(i) + 2 hat(j) -3 hat(k)`, then (Q) `V_1 +V_2 +V_3 =60`
(C) If `V_1, V_2,V_3` are the volumes of parallelopiped, triangular prism and tetrahedron respectively. The three coterminus edges of all three figures are the vectors `-3hat(i) + hat(j) + hat(k) ,4 hat(i) +2 hat(j)+ 4 hat(k)` and `2 hat(i) + 2 hat(j)`, then (R) `V_1 +3V_3 =3V_2`
(S) `V_1 +V_2 +V_3 =50`
(T) `V_1 : V_2 : V_3 = 6 : 3 : 1`
A

`A-> (P, R, S, T); B -> (P, R, T); C -> (P, Q, R, T)`

B

`A-> (P, R, S, Q); B -> (P, S, T); C -> (P, Q, R, T)`

C

`A-> (P, R, Q, T); B -> (P, R, T); C -> (S, Q, R, T)`

D

`A-> (P, R, S, T); B -> (P, Q, T); C -> (P, S, R, T)`

HINT


Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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