Question

What is addition of vectors (Analytical method)?​

Answer 1

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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Answer 2

$\large{\underline{\textrm{Addition of vectors by Analytical method:-}}}$

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∅