Question

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define the triangle law of vector addition and Prove it also​

Answer 1

Triangle Law:

= It states that if two vectors acting simultaneously at a point are represented in magnitude and direction by the two sides of a triangle taken in same order. And their resultant is represented in magnitude and direction by the third side of the triangle taken in opposite order.

→ [Diagram is in attachment]

Prove

Consider two vectors A vector and B vector represented by OP and PQ. Let the angle between A vector and B vector is Q (theta) by the two sides of a triangle. Resultant to be OD vector by third side of triangle taken in opposite order. Draw DN perpendicular to OP produced.

Magnitude of R vector

In triangle OND (By Pythagoras)

(R)² = (ON)² + (ND)²

(R)² = (OP + PN)² + (ND)²

(R)² = (A + PN)² + (NQ)² . ..(S)

In A PDN

PN÷PD = Cos Q

PN÷B Cos Q -

PN=B Cos Q .... (1)

ND÷PQ = Sin Q

ND÷B Sin Q

ND = B Sin Q... (2)

Put value of (1) and (2) in (S)

(R)² = (A + B Cos Q)² + (B Sin Q)²

(R)² = A²+ B² Cos²Q + 2AB Cos Q + B² Sin² Q

R = VA²+ B² (Sin2Q + Cos²Q) + 2AB CosQ

R = √A²+ B² + 2AB Cos Q

Direction of R vector

_

Let R vector make an angle | | with A vector.

tan= DN : ON

B Sin Q÷OP + PN

= B Sin Q÷A + B Cos Q

Answer 2

Answer:

I hope it helps you

for answer check out the above image