Resultant magnitude is 30N and direction is tan inverse 1/2 with 20N vector.

Calculation of Resultant and Direction of Resultant:

Given:
Magnitude of the first vector (V1) = 10N
Magnitude of the second vector (V2) = 20N

Finding the Resultant Vector:
To find the resultant vector, we can use the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using this theorem, we can calculate the magnitude (R) of the resultant vector:
R^2 = V1^2 + V2^2
R^2 = 10^2 + 20^2
R^2 = 100 + 400
R^2 = 500
R = √500
R ≈ 22.36N (rounded to two decimal places)

Finding the Direction of the Resultant Vector:
To determine the direction of the resultant vector, we can use trigonometry. In this case, we have a right-angled triangle with one side (V1) along the x-axis and the other side (V2) along the y-axis. The resultant vector (R) will be the hypotenuse of this triangle.

We can find the angle (θ) between the resultant vector and the second vector (V2) using the tangent function:
tan(θ) = V1/V2
tan(θ) = 10/20
tan(θ) = 0.5
θ ≈ 26.565° (rounded to three decimal places)

Since the second vector is at a right angle to the first vector, the direction of the resultant vector will be the angle between the second vector (V2) and the x-axis, which is 90°.

Therefore, the resultant vector has a magnitude of approximately 22.36N and is directed at an angle of approximately 26.565° with the second vector, in the direction perpendicular to the x-axis.