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Combination

If OABC is ...

Question

If $O A B C$ is a parallelogram with $\to O B = \to a, \to A B = \to b$ then $\to O A =$

A

\to a + \to b

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B

\to a - \to b

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C

\frac{1}{2} (\to a + \to b)

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D

\frac{1}{2} (\to a - \to b)

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Solution

The correct option is C $\to a - \to b$
From figure we get
$- - \to O A + - - \to A B = - - \to O B$
$- - \to O A = \to a - \to b$

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Q. Assertion :In

Δ

\to A B + \to B C + \to C A = 0

\to O A = \to a, \to O B = \to b

\to A B = \to a + \to b

\to a, \to b, \to c

be three vectors such that

| \to a + \to b + \to c | = 1, \to c = λ (\to a \times \to b)

| \to a | = \frac{1}{\sqrt{2}}, | \to b | = \frac{1}{\sqrt{3}}, | \to c | = \frac{1}{\sqrt{6}}

, then the angle between

\to a

\to b

\to a, \to b

| \to a | = \sqrt{3}, | \to b | = 2

(\to a, \to b) = \frac{π}{3}

. Then the area of the triangle with adjacent sides

\to a + 2 \to b

2 \to a + \to b

(\to A - \to B) \times (\to A + \to B)

2 (\to A \times \to B)

(\to a - \to b) \times (\to a + \to b) = 2 (\to a \times \to b)

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