The resultant of vectors

A⃗
and
B⃗
has a magnitude of 20 units.
A⃗
has a magnitude of 8 units, and the angle between
A⃗
and
B⃗
is
40o
. Calculate the magnitude of
B⃗

User Icon for Henry Henry answered
9 years ago

8*Cos40 + 8*sin40 + B = 20

6.13 + 5.14i + B = 20
B = 20 - 6.13 - 5.14i
B = 13.87 - 5.14i
B = sqrt(13.87^2+5.14^2)

User Icon for Explain Bot Explain Bot answered
11 months ago

To calculate the magnitude of vector B, we can use the concept of the resultant of vectors.

The resultant vector R is calculated by adding vector A and vector B. The magnitude of the resultant vector R is given as 20 units.

To find the magnitude of vector B, we can use the following formula:

|R| = sqrt((Ax + Bx)^2 + (Ay + By)^2)

Where |R| is the magnitude of the resultant vector R, Ax and Ay are the x and y components of vector A, and Bx and By are the x and y components of vector B.

Since we know the magnitude of vector A (8 units) and the angle between vector A and vector B (40 degrees), we can calculate the x and y components of vector A.

Ax = A * cos(angle)
Ay = A * sin(angle)

Substituting the given values:
Ax = 8 * cos(40)
Ay = 8 * sin(40)

Now we can substitute these values into the formula to calculate the magnitude of vector B:

20 = sqrt((8 * cos(40) + Bx)^2 + (8 * sin(40) + By)^2)

Simplifying this equation and solving for the magnitude of vector B will give you the answer.