Question

explain triangle method of vector addition ​

Answer 1

Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.

Consider two vectors P and Q that are represented in the order of magnitude and direction by the sides OA and AB, respectively of the triangle OAB. Let R be the resultant of vectors P and Q

R=P+Q

From triangle OCB,

OB2=OC2+BC2 OB2=(OA+AC)2+BC2 (eq.1)

In triangle ACB with ϴ as the angle between P and Q

cosΘ=ACAB AC=ABcosΘ=QcosΘ sinΘ=BCAB BC=ABsinΘ=QsinΘ R2=(P+QcosΘ)2+(QsinΘ)2 (after substituting AC and BC in eq.1)

R2=P2+2PQcosΘ+Q2cos2Θ+Q2sin2Θ R2=P2+2PQcosΘ+Q2

therefore, R=P2+2PQcos

Answer 2

The triangle-based law of vector addition is the most frequently used method to determine the magnitude and direction of the resultant vector.

Triangle law of vectors

• The law says that, if the two vectors whose resultant is to be found, are put together in the form of the two edges of the triangle, then the resultant vector is depicted as the third side of the  triangle but in the reverse order,

• Let us consider A and B as the two vectors. We need to find their resultant. The two vectors are joined together as the sides of the triangle. The resultant is given by the third side.
• The formula is:

                  vector(A) + vector(B)= vector(R)

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