In a triangle ABC- if 2A-C- -3C-B- then 2O-A- -3O-B- equals -

The correct option is A 5O⃗C⃗ [ Given in Δ ABC,; 2 AB =3 CB, #160;; 2 ...

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Addition of Vectors

In a triangle...

Question

In a triangle ABC, if $2 \to A C = 3 \to C B$ , then $2 \to O A + 3 \to O B$ equals ?

5 \to O C

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- \to O C

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\to O C

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None of these

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Solution

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

A B C D

O

\to O A + \to O B + \to O C + \to O D

\to O A = 3 i + 4 j + 12 k, \to O B = 12 i + 3 j + 4 k,

\to O C = 4 i + 12 j + 3 k .

\to O A

\to O C .

\to O A, \to O B

\to O C

R (1 + \sqrt{2})

R

∠ A O B = ∠ B O C = 45^{\circ}

\to O A + \to O C

\to O B

(\to O A + \to O C) + \to O B

\to O B

⎡ ⎢ ⎢ ⎣ \begin{matrix} \to O A \times \to O B =^i -^j +^k \to O B \times \to O C =^i \to O C \times \to O A = -^i +^j \end{matrix} ⎤ ⎥ ⎥ ⎦

∣ ∣ \to C A \times \to C B ∣ ∣

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