If a- and b-2k- Find a-b-a-2b-

Given, nbsp;a=î+ĵ and nbsp;b= ĵ+2k̂ a b= (î+ĵ) ( ĵ+2k̂)=î+2ĵ 2k̂ and a+2b= (î+ĵ)+2( ĵ+2k̂)= î ĵ+4k̂ Thus, (a b).(a+2b)= (î+2ĵ 2k̂).(î ĵ+4k̂) ⇒ 1 2 8= 9 ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If a=î+ĵ and ...

Question

If $\to a =^i +^j$ and $\to b = -^j + 2^k$ . Find $(\to a - \to b) . (\to a + 2 \to b)$ .

6

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- 6

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9

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- 9

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Solution

The correct option is D $- 9$
Given, $\to a =^i +^j$ and $\to b = -^j + 2^k$
$\to a - \to b = (^i +^j) - (-^j + 2^k) =^i + 2^j - 2^k$
and $\to a + 2 \to b = (^i +^j) + 2 (-^j + 2^k) =^i -^j + 4^k$
Thus, $(\to a - \to b) . (\to a + 2 \to b) = (^i + 2^j - 2^k) . (^i -^j + 4^k)$
$\Rightarrow 1 - 2 - 8 = - 9$

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If →a=^i+^j and →b=−^j+2^k. Find (→a−→b).(→a+2→b).

The correct option is D −9Given, →a=^i+^j and →b=−^j+2^k →a−→b=(^i+^j)−(−^j+2^k)=^i+2^j−2^k and →a+2→b=(^i+^j)+2(−^j+2^k)=^i−^j+4^k Thus, (→a−→b).(→a+2→b)=(^i+2^j−2^k).(^i−^j+4^k) ⇒ 1−2−8=−9

If $\to a =^i +^j$ and $\to b = -^j + 2^k$ . Find $(\to a - \to b) . (\to a + 2 \to b)$ .