Let a-k- b-3-k- and c-2-k- where - and - are integers- If a-b-1 and b-c-10- then a-b -c is equal to

A·b= 1 ⇒ 3 2αβ = 1 ⇒αβ =2 …(1) nbsp; b·c=10 ⇒ 3α 2β α=10 ⇒ 2α +β = 5 …(2) From (1) and (2) Clearly, (α ,β )=( 2, 1) [ a b c ]= nbsp;1 amp;2 ...

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Subtraction of a Vector

Let a=î-αĵ+βk...

Question

Let $\to a =^i - α^j + β^k,$ $\to b = 3^i + β^j - α^k$ and $\to c = - α^i - 2^j +^k$ , where $α$ and $β$ are integers. If $\to a \cdot \to b = - 1$ and $\to b \cdot \to c = 10,$ then $(\to a \times \to b) \cdot \to c$ is equal to

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3 \sqrt{2},

(\to c - (\to a \times \to b)) . \to c

1

\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k

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| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243

2

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |

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