Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C = 2A - B
Answer:
22.24° to the positive x-axis.
Given vectors:
A (5, 6)
B (-12, 3)
C = 2A - B ------------(i)
First let's represent the two vectors in unit notation as follows;
A = 5 i + 6 j
B = -12 i + 3 j
Now substitute these vectors into equation (i) as follows;
C = 2(5 i + 6 j) - (-12 i + 3 j)
C = 2(5 i + 6 j) + (12 i - 3 j)
C = 10 i + 12 j + 12 i - 3 j [collect like terms]
C = 10 i + 12 i + 12 j - 3 j
C = 22 i + 9 j ----------------(ii)
The direction, θ, of vector C can be calculated as follows;
θ = tan⁻¹([tex]\frac{9}{22}[/tex])
θ = tan⁻¹(0.409)
θ = 22.24°
Since both the x and y components of vector C are positive, the direction of the vector is 22.24° to the positive x-axis.
