OABC is a tetrahedron- then express the vectors OA-OB and CA in terms of the vectors OC-AB and BC

The correct option is C OA= OC AB BC ; OB= OC BC ; CA= AB BC OABC is a tetrahedron.Expressing the vectors OA,OB and CA in terms of the vecto ...

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Standard XII

Physics

Vector Addition

OABC is a tet...

Question

OABC is a tetrahedron, then express the vectors $- - \to O A, - - \to O B a n d - - \to C A$ in terms of the vectors $- - \to O C, - - \to A B a n d - - \to B C$

- - \to O A = - - \to O C + - - \to A B + - - \to A C; - - \to O B = - - \to O C - - - \to B C; - - \to C A = - - \to A B - - - \to B C

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- - \to O A = - - \to O C - - - \to A B - - - \to A C; - - \to O B = - - \to O C + - - \to B C; - - \to C A = - - \to A B - - - \to B C

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- - \to O A = - - \to O C - - - \to A B - - - \to B C; - - \to O B = - - \to O C - - - \to B C; - - \to C A = - - - \to A B - - - \to B C

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none of these

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Solution

The correct option is C $- - \to O A = - - \to O C - - - \to A B - - - \to B C; - - \to O B = - - \to O C - - - \to B C; - - \to C A = - - - \to A B - - - \to B C$
$O A B C$ is a tetrahedron.
Expressing the vectors $- - \to O A, - - \to O B a n d - - \to C A$
in terms of the vectors $- - \to O C, - - \to A B a n d - - \to B C$
$- - \to O A = - - \to O C + - - \to C A$
$= - - \to O C + - - \to C B + - - \to B A$
$= - - \to O C - - - \to B C - - - \to A B$
$- - \to O B = - - \to O C + - - \to C B = - - \to O C - - - \to B C$
$- - \to C A = - - \to C B + - - \to B A = - - - \to B C - - - \to A B$
Hence, option C.

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Similar questions

If $O$ is a point within triangle $A B C$ , show that,

$If O is a point within Δ A B C, show that (i) AB + AC > O B + O C (ii) AB + BC + CA > O A + O B + O C (iii) OA + OB + OC > \frac{1}{2} (A B + B C + C A .)$

Q. If

O

is a point within

Δ

ABC then show that :
1)

A B + A C = O B + O C

A B + B C + C A > O A + O B + O C

O A + O B + O C > \frac{1}{2} (A B + B C + C A)

O is any point in the interior of $Δ A B C .$

Prove that

$(i) A B + A C > O B + O C$

$(i i) A B + B C + C A > O A + O B + O C$

$(i i i) O A + O B + O C > \frac{1}{2} (A B + B C + C A)$

. O is any point in the interior of a triangle ABC. Prove that

1. AB + AC > OB + OC

2.AB + BC + CA > OA + OB + OC

3.OA + OB + OC > 1/2(AB + AC + BC)

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OABC is a tetrahedron, then express the vectors −−→OA,−−→OBand−−→CA in terms of the vectors −−→OC,−−→ABand−−→BC

OABC is a tetrahedron, then express the vectors $- - \to O A, - - \to O B a n d - - \to C A$ in terms of the vectors $- - \to O C, - - \to A B a n d - - \to B C$