Resultant Vector Formula

About Resultant Vector Formula

To get the resultant value of two or more vectors, apply the resultant vector formula. This is accomplished by computing the vectors based on their relative directions. The resultant vector formula is useful in physics and engineering.

What do you mean by Resultant Vector Formula?

Based on the orientation of the vectors, the resultant vector formula has three types. These formulas apply to vectors moving in the same direction, vectors moving in the opposite direction, and vectors moving in the same direction but at an angle to each other.

Formula:

To get the resultant vector, simply add vectors in the same direction. A and B are the same-direction vectors, while R is the resulting vector. R = A + B

Formula:

To obtain the resultant vector, vectors in opposite directions are subtracted from each other. The consequent vector R is the vector B, which is in the opposite direction of the vector A. R = A - B

Formula:

To obtain the resultant vector, compute vectors inclined to each other using the formula below. R is the resultant vector, and A and B are inclined at an angle “Ø” to each other.

R2 = A2 + B2 + 2ABCosØ

Solved example of Resultant Vector Formula

Example: Find resultant of the vectors 4i + 3j -5k and 8i + 6j - 10k.

  1. Sol: It is given that the two vectors are:
  2. A = 4i + 3j - 5k and B = 8i + 6j - 10k
  3. Direction ratios of two vectors are in equal proportion and thus two vectors are in same direction.
  4. Following resultant vector formula can be used here.
  5. R = A + B
  6. = (4i + 3j - 5k) + (8i + 6j - 10k)
  7. = 12i + 9j - 15k

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Resultant Vector Formula

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