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The volume of the tetrahedron whose co-t...

The volume of the tetrahedron whose co-terminous edges are `overline(a), overline(b), overline(c)`, where `overline(a), overline(b), overline(c)` are non-coplanar units vectors each inclined with other at an angle of `30^(@)` is

A

`(3sqrt(3)-5)/(12)`cu. units

B

`(3sqrt(3)-5)/(144)`cu. Units

C

`(sqrt(3sqrt(3)-5))/(12)`cu. Units

D

`(sqrt(3sqrt(3)-5))/(144)`cu. Units

Text Solution

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The correct Answer is:
C
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[[overline(a), overline(b)+overline(c), overline(c)+overline(b)+overline(a)]]=

If overline(c)=3overline(a)-2overline(b) , then [[overline(a), overline(b), overline(c)]]=

[[overline(a), overline(b), overline(a)timesoverline(b)]]=

[[overline(a)-overline(b), overline(b)-overline(c), overline(c)-overline(a)]]=

[[overline(a)+overline(b), overline(b)+overline(c), overline(c)+overline(a)]]=

If overline(a) and overline(b) are parallel vectors [[overline(a), overline(b), overline(c)]] =

overline(a)*((overline(a)+overline(b)+overline(c))times(overline(b)+overline(c)))=

Value of ((overline(a)+overline(b)+overline(c))times(overline(b)-overline(a)))*overline(c) is

|[overline(a)*overline(a), overline(a)*overline(b)], [overline(a)*overline(b), overline(b)*overline(b)]|=

NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. The volume of the tetrahedron whose co-terminous edges are hat(j)+hat...

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  2. Find the volume tetrahedron whose coterminus edges are 7hat(i)+hat(k),...

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  3. The volume of the tetrahedron whose co-terminous edges are overline(a)...

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  4. Volume of tetrahedron with vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0)...

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  5. The volume of the tetrahedron whose vertices are A(-1, 2, 3), B(3, -2,...

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  6. The volume of the tetrahedron whose vertices are (3, 7, 4), (5, -2, 3)...

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  7. If overline(a)*hat(i)=4, then (overline(a)timeshat(j))*(2hat(j)-3hat(k...

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  8. If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3...

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  9. [[hat(i), hat(j), hat(k)]]+[[hat(k), hat(j), hat(i)]]+[[hat(j), hatk, ...

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  10. If overline(u)=hat(i)-2hat(j)+hat(k), overline(v)=3hat(i)+hat(k), over...

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  11. If overline(u)=hat(i)-2hat(j)+hat(k), overline(v)=3hat(i)+hat(k), over...

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  12. If overline(a)=hat(i)+5hat(k), overline(b)=2hat(i)+3hat(k), overline(c...

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  13. If overline(u)=-hat(i)-2hat(j)+hat(k), overline(r)=3hat(i)+hat(k), ove...

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  14. If overline(c)=3overline(a)-2overline(b), then [[overline(a), overline...

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  15. [[overline(a), overline(b), overline(a)timesoverline(b)]]=

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  16. Which of the following is trues?

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  17. [[overline(a)-overline(b), overline(b)-overline(c), overline(c)-overli...

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  18. If overline(a), overline(b) and overline(c) are unit coplanar vectors,...

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  19. If overline(a), overline(b) and overline(c) are three non-coplanar vec...

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  20. [[overline(a)+overline(b), overline(b)+overline(c), overline(c)+overli...

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