If-A-2-3-and-B-4-2-then-A-B- -

A=2î 3ĵ B= 4î+2ĵ, A· nbsp;B=(2î 3ĵ).( 4î+2ĵ) =(2 nbsp;× 4)(î·î)+(2 × 2)(î·ĵ)+(3 × 4)(ĵ·î) (3 × 2)(ĵ·ĵ) Now î·î=ĵ·ĵ =1(|î||î| cos 0=1) î· nbsp;ĵ = ĵ· n ...

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Byju's Answer

Standard XII

Mathematics

Dot Product of Two Vectors

If A=2î-3ĵ an...

Question

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

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Solution

$\to A = 2^i - 3^j \to B = - 4^i + 2^j, \to A \cdot \to B = (2^i - 3^j) . (- 4^i + 2^j)$

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

$Now^i \cdot^i =^j \cdot^j = 1 (|^i | |^i | cos 0 = 1)$

$^i \cdot^j =^j \cdot^i = 0$ ( $^i$ 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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If →A=2^i−3^j and →B=−4^i+2^j, then |→A.→B|= ___

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