Question

1. Two vectors ( vec{a} ) and ( vec{b} ), have a common starting point with an angle of ( 150∘) between them. Vector ( vec{a}=5 ) and ( vec{b}=7 ). Calculate ( vec{a}+vec{b}

Answer 1

To calculate the sum of two vectors with a common starting point and an angle between them, use the vector addition method. Substitute the given values into the formula to find the magnitude of the sum.

Step-by-step explanation:

To calculate the sum of two vectors, we can use the vector addition method.

Since the vectors have a common starting point and an angle of 150 degrees between them, we can use the cosine law to find the magnitude of the sum of the vectors.

It is given by the equation:

|A + B| = sqrt(A^2 + B^2 + 2ABcos(angle))

Substituting the given values, we get:

|vec{a} + vec{b}| = sqrt(5^2 + 7^2 + 2(5)(7)cos(150)) = sqrt(25 + 49 - 70) = sqrt(4) = 2 units

mathematics

Physics

Vector addition