Three vectors A- - B- and C- are such that A- - B- - C- and their magnitudes are 5-4 and 3 respectively- Find the angle between A- and C-

Given C = A + B A =5 B =4 C =3 | C #160; | #160; ^ 2 =| A #160; | #160; ^ 2 +| B #160; | #160; ^ 2 +2 A . B cosθ ...

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Byju's Answer

Standard XII

Mathematics

Dot Product of Two Vectors

Three vectors...

Question

Three vectors $\to A, \to B$ and $\to C$ are such that $\to A + \to B = \to C$ and their magnitudes are $5, 4$ and $3$ respectively. Find the angle between $\to A$ and $\to C$

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Solution

Given $\to C = \to A + \to B$
$\to A = 5 \to B = 4 \to C = 3 {∣ ∣ ∣ \to C ∣ ∣ ∣}^{2} = {∣ ∣ ∣ \to A ∣ ∣ ∣}^{2} + {∣ ∣ ∣ \to B ∣ ∣ ∣}^{2} + 2 \to A . \to B cos θ g = 25 + 16 + 2 \times 5 \times 4 \times cos θ cos θ = \frac{32}{2 \times 5 \times 4} cos θ = \frac{4}{5} θ = {c o s}^{- 1} \frac{4}{5}$

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Three vectors →A,→B and →C are such that →A+→B=→C and their magnitudes are 5,4 and 3 respectively. Find the angle between →A and →C

Given →C=→A+→B→A=5→B=4→C=3∣∣∣→C∣∣∣2=∣∣∣→A∣∣∣2+∣∣∣→B∣∣∣2+2→A.→Bcosθg=25+16+2×5×4×cosθcosθ=322×5×4cosθ=45θ=cos−145

Three vectors $\to A, \to B$ and $\to C$ are such that $\to A + \to B = \to C$ and their magnitudes are $5, 4$ and $3$ respectively. Find the angle between $\to A$ and $\to C$