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If a,b,c are there given non-coplanar ve...

If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, `Delta_(1) =|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}|, Delta_(2)=|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}|, Delta_(3) =|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}|, Delta=|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}|`
The value of `|{:(a,b,c),(a.p,b.p,c.p),(a.q,b.q,c.q):}|` is:

A

`(p xx q)[a xx b.b xx c, c xx a]`

B

`2(p xx q)[a xx b, b xx c, c xx a]`

C

`4(p xx q)[a xx b, b xx c , c xx a]`

D

`(p xx q)sqrt([a xx b b xx c c xx a])`

Text Solution

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The correct Answer is:
D
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