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Let ` vec a , vec ba n d vec c` be three non-coplanar vecrors and ` vec r` be any arbitrary vector. Then `( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b)` is always equal to `[ vec a vec b vec c] vec r` b. `2[ vec a vec b vec c] vec r` c. `3[ vec a vec b vec c] vec r` d. none of these

A

`2[vec(a),vec(b),vec(c)]vec(r)`

B

`3[vec(a), vec(b),vec(c)]vec(r)`

C

`[vec(a), vec(b),vec(c)] vec(r)`

D

none of these

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MOTION-VECTOR -EXERCISE - 2 ( LEVEL -I)
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  4. Let vec(u) = hat(i) + hat(j), vec(v) = hat(i) - hat(j) and vec(w) = h...

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  6. If vec a =vec b +vec c,vec b xx vec d =vec 0 ,vec c *vec d = 0 then ...

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  7. Consider a tetrahedron with faces f1, f2, f3, f4. Let vec a1, vec a2...

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  8. Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(...

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  12. Let vec r be a vector perpendicular to vec a + vec b+ vec c, where [ve...

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  13. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equal...

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  14. If the vectors a hat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k) and hat(i...

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  15. (vec(d) + vec(a)).(vec(a) xx (vec(b) xx (vec(c) xx vec(d)))) simplifie...

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  17. Let vec a , vec ba n d vec c be three non-coplanar vecrors and ve...

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  18. The vectors vec(a) = - 4hat(i) + 3hat(k), vec(b)

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