Grade 11 - Algebraic Method of Addition of Vectors in Two Dimensions

Topic: Algebraic Method of Addition of Vectors

In the algebraic method, vectors are added by breaking them into components along the x and y axes.
Steps:

1. Resolve each vector into components:
Ax, Ay, Bx, By.

2. Add corresponding components:
Rx = Ax + Bx
Ry = Ay + By

3. Find the resultant vector:
R = sqrt(Rx^2 + Ry^2)

4. Determine the angle theta:
theta = tan^(-1)(Ry / Rx)

This method allows precise calculation without needing a graphical representation.

Challenging Questions:
1. What is the x-component of a vector with magnitude 10 units at an angle of 30 degrees to the positive x-axis?
a) 5 units
b) 10 * cos(30 degrees)
c) 10 units
d) 10 * sin(30 degrees)

2. If two vectors have components A = 3i + 4j and B = 5i - 2j, what is their resultant vector?
a) 8i + 2j
b) -2i + 6j
c) 8i - 6j
d) 2i + 2j

3. What is the magnitude of the resultant vector from the previous question?
a) 10 units
b) sqrt(68) units
c) sqrt(52) units
d) 6 units

4. Which trigonometric function is used to find the direction of the resultant vector?
a) Sine
b) Cosine
c) Tangent
d) Secant

5. What is the effect of multiplying a vector by a scalar of -1?
a) Doubles its magnitude
b) Changes its direction
c) Reduces its magnitude by half
d) Makes it zero

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