Vector a⃗ points in the negative y direction and has a magnitude of 7 units. vector b⃗ has twice the magnitude and points in the positive x direction.

find the direction and magnitude of a⃗ +b⃗ .
express your answer as a whole number.

The magnitude of the vector is and the direction of the vector is

Further Explanation:

points in the negative Y-direction and has a magnitude of , so we will show it as a line of length in negative Y-direction.

has twice the magnitude and points in the positive X-direction, so we will show it by a line of double the length as before in positive X-direction, as shown in the figure below.

According to Cartesian coordinate system, the resultant will start either from tail of and ends at head of and vice-versa.

Now, resultant will be given by  

Hence, the magnitude of resultant or of vector is given by:

It can be expressed in whole number as:

Now, the direction of the resultant vector or of the vector is given by:

Now, substituting the values of vector and :

Thus, the magnitude of the vector is and the direction of the vector is

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Vectors and Scalars

Keywords:

Vector, scalars, vector A, Vector B, addition, resultant, unit, magnitude, direction, positive, X-axis, Y- axis, negative, 7 units, 14 units, twice the magnitude.

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