Problem:
A vector A makes an angle of 20 degree and B makes an angle of 110 degree with the x axis. The magnitude of these vectors are 3 m and 4 m respectively. Find the resultant? Explain in details.

Solution:
To find the resultant of two vectors A and B, we need to add these vectors together. We can use the law of cosines to find the magnitude and direction of the resultant vector.

Step 1: Convert angles to radians
We need to convert the angles to radians by multiplying them by π/180.

Angle of vector A = 20° x π/180 = 0.349 rad
Angle of vector B = 110° x π/180 = 1.919 rad

Step 2: Find the x and y components of each vector
We can find the x and y components of each vector using trigonometry.

x-component of vector A = 3 cos 20° = 2.817 m
y-component of vector A = 3 sin 20° = 1.034 m

x-component of vector B = 4 cos 110° = -1.301 m
y-component of vector B = 4 sin 110° = 3.695 m

Step 3: Add the x and y components of the vectors
We can add the x and y components of the vectors to find the x and y components of the resultant vector.

x-component of resultant vector = 2.817 m - 1.301 m = 1.516 m
y-component of resultant vector = 1.034 m + 3.695 m = 4.729 m

Step 4: Find the magnitude and direction of the resultant vector
We can use the Pythagorean theorem to find the magnitude of the resultant vector.

Magnitude of resultant vector = √(1.516² + 4.729²) = 4.914 m

We can use the inverse tangent function to find the direction of the resultant vector.

Direction of resultant vector = tan⁻¹(4.729/1.516) = 73.821°

Step 5: Conclusion
The resultant vector has a magnitude of 4.914 m and makes an angle of 73.821° with the x-axis.

ACCORDING TO GIVEN DATA THETA 1 IS 20 AND THETA 2 IS 110. SO THE ANGLE BETWEEN TWO VECTORS IS 90. TO FIND RESULATANT JUST TAKE ROOT OF SUM OF MAGNITUDE OF EACH VECTOR.
R=√(4)^2+(3)^2
R=5m