If a and b are two vectors- then the value of a - b - a - b is

(a b) × (a + b) = a×a + a×b b×a b×b = 0 + (a×b) + (a×b) + 0 = 2(a×b) [∵a×b = b̂×a, a×a = b×b = 0] ...

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Linear Combination of Vectors

If a and b ar...

Question

If $\to a$ and $\to b$ are two vectors, then the value of $(\to a - \to b) \times (\to a + \to b)$ is

(\to a \times \to b)

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2 (\to a \times \to b)

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3 (\to a + \to b)

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\to 0

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Solution

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\to a

\to b

| \to a | = | \to b |,

| \to a + \to b | + | \to a - \to b |

\to A

\to B

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

\to a

\to b

| \to a | = 6, | \to b | = 3

\to a \cdot \to b = 9,

| \to a \times \to b |

\to a, \to b

| \to a \times \to b | = 2,

[\begin{matrix} \to a & \to b & \to a \times \to b \end{matrix}]

\to a, \to b

\to c

\to a + \to b + \to c = 0

(\to a . \to b + \to b . \to c + \to c . \to a)

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