What is addition of vectors (Analytical method)?
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Answer:
The analytical method of vector addition and subtraction involves using the Pythagorean theorem and trigonometric identities to determine the magnitude and direction of a resultant vector.
Explanation:
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[tex]\large{\underline{\textrm{Addition of vectors by Analytical method:-}}}[/tex]
Proof:—
(figure in the attachment provided)
In ∆ADC by Pythagoras Theorem
→ AC²= AD²+DC²
→ AC²= (AB+BD)²+DC²
→ AC²= AB²+BD²+2AB.BD
→ BD²+DC²= BC²
→ AC²= AB²+BC²+2AB.BD....(1)
Now,
→AC²= AD²+DC²
→ (AB+BD)²+DC²
∆BDC
→cos∅= BD/BC
→ BD = BC cos∅
AC²= AB²+BC²+2AB.BC cos∅
→ R²= P²+Q²+2PQ cos∅
→ R = √(P²+Q²+2PQcos∅)
In ∆ADC
→ tan¢ = DC/AC
→ tan¢ = DC/AB+BD......(2)
In ∆BDC,
→ sin∅= DC/BC
→ DC = BC sin ∅....(3)
→ BD= BC cos∅....(3)
putting eqⁿ (3) inti (2)
→ tan¢ = BC sin∅/AB+BC cos∅
→ tan¢ = Qsin∅/P+Qcos∅