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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

User Uzzar
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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

When two vectors À and B are drawn from a common point, the angle between them is-example-1