If A-2 -3 - and B-4 -2 - then -A-B-A- 14B- 2C- 16

The correct option is A 14A=2î 3ĵ B= 4î+2ĵ, A.B=(2î 3ĵ).( 4î+2ĵ) =(2 × 4)(î.î)+(2 × 2)(î. ĵ)+(3 × 4)(ĵ.î) (3 × 2)(ĵ.î) Now î.î=ĵ.ĵ =1(|î||î| cos 0=1) î . ĵ = ...

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Byju's Answer

Standard XII

Mathematics

Dot Product of Two Vectors

If A⃗=2 î-3 ĵ...

Question

If $\to A = 2^i - 3^j$ and $\to B = - 4^i + 2^j$ , then $| \to A . \to B |$ =

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Solution

The correct option is A 14
$\to A = 2^i - 3^j \to B = - 4^i + 2^j, \to A . \to B = (2^i - 3^j) . (- 4^i + 2^j)$

$= (2 \times - 4) (^i .^i) + (2 \times 2) (^i .^j) + (3 \times 4) (^j .^i) - (3 \times 2) (^j .^i)$

$N o w^i .^i =^j .^j = 1 (|^i | |^i | cos 0 = 1)$

$^i .^j =^j .^i = 0$ ( $^i$ and $^j$ are perpendicular to each other)

So $(2^i - 3^j) . (- 4^i + 2^j)$

= -8 + 0 + 0 – 6

= -14

$| \to A . \to B | = | - 14 | = 14$

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\sqrt{78}

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If →A =2^i−3^j and →B =−4^i+2^j, then |→A.→B| =

If $\to A = 2^i - 3^j$ and $\to B = - 4^i + 2^j$ , then $| \to A . \to B |$ =