The resultant of the two vectors A and B drawn from common point is V² = A² + B² - (2AB) x cos(D).
How to calculate the resultant vector?
For the given vector A and vector B drawn from the same point, the magnitude of the resultant vector V is calculated by applying parallelogram law of vector addition.
From triangle PQT, the value of side length PQ is calculated by applying Cosine rule as follows;
PQ² = PT² + QT² - (PT x QT) cos(D)
where;
- line PQ = V
- line PT = A
- line QT = B
V² = A² + B² - (2AB) x cos(D), shown
The complete question is below:
When Two Vectors À And B Are Drawn From A Common Point, The Angle Between Them Is D. (A) Using Vector Techniques, Show That The Magnitude Of Their Vector Sum Is Given By V = A² + B² - 2AB Cos D
D⁰