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

### Question Asked by a Student from EXXAMM.com Team

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

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

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