If A-9-7-5k- and B-3-2-6k- then the value of A-B-A-B is

Given, nbsp;A=9î 7ĵ+5k̂ nbsp; and nbsp;B=3î 2ĵ 6k̂ So, we have nbsp; A+B= 12î 9ĵ k̂ and, A B= 6î 5ĵ+11k̂ Thus, from the dot product we have (A+B)·(A B)= ...

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Byju's Answer

Standard XIII

Physics

Multiplication with Vectors

If A=9î-7ĵ+5k...

Question

If $\to A = 9^i - 7^j + 5^k$ and $\to B = 3^i - 2^j - 6^k$ , then the value of $(\to A + \to B) \cdot (\to A - \to B)$ is

206

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128

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106

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Solution

The correct option is C $106$
Given, $\to A = 9^i - 7^j + 5^k$ and $\to B = 3^i - 2^j - 6^k$
So, we have
$\to A + \to B = 12^i - 9^j -^k$
and, $\to A - \to B = 6^i - 5^j + 11^k$
Thus, from the dot product we have
$(\to A + \to B) \cdot (\to A - \to B) = (12^i - 9^j -^k) \cdot (6^i - 5^j + 11^k)$
$\Rightarrow (\to A + \to B) \cdot (\to A - \to B) = 72 + 45 - 11 = 106$

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Similar questions

Q. If

\to A = 9^i - 7^j + 5^k

and

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

, then the value of

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

Q. lf

\to a = 9^i - 7^j + 5^k

and

\to b = 3^i - 2^j - 6^k

, then the value of

(- \to a + \to b)

(- \to a - \to b)

is:

Q. If

\to A = 2^i + 7^j + 3^k

and

\to B = 3^i + 2^j + 5^k

, then find the projection of

\to a

\to b

Q. If

\to A = 2^i + 7^j + 3^k

and

\to B = 3^i + 2^j + 5^k

, find component of

\to A

along

\to B .

| \to a \times \to b |

\to a =^i - 7^j + 7^k

and

\to b = 3^i - 2^j + 2^k

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If →A=9^i−7^j+5^k and →B=3^i−2^j−6^k, then the value of (→A+→B)⋅(→A−→B) is

The correct option is C 106Given, →A=9^i−7^j+5^k and →B=3^i−2^j−6^k So, we have →A+→B=12^i−9^j−^k and, →A−→B=6^i−5^j+11^k Thus, from the dot product we have (→A+→B)⋅(→A−→B)=(12^i−9^j−^k)⋅(6^i−5^j+11^k) ⇒ (→A+→B)⋅(→A−→B)=72+45−11=106

If $\to A = 9^i - 7^j + 5^k$ and $\to B = 3^i - 2^j - 6^k$ , then the value of $(\to A + \to B) \cdot (\to A - \to B)$ is