Vector A, B and C have magnitude 5, 7.071 and 5 respectively, directions of A, B and C are towards
east, North-East and North respectively. If i and j are unit vectors along East and North respectively,
express the sum A+B+C in terms of i, j. Also find magnitude and direction of the resultant
Answers
Answer:
Sum = 12.071(i +j)
Magnitude = 17.07
Resultant = 45° or π/4 radians
Explanation:
As shown in the figure attached below, consider an x-y plane and take North on the positive y-axis and South on the negative y-axis opposite to each other and East on the positive x-axis and West on the negative x-axis. We are given, i and j as unit vectors along East and North respectively.
Directions of A is towards East, B is towards North-East and C is towards North.
Therefore, we can write the A, B & C vectors as
Vector A = 5i
Vector B = 7.071(i + j)
Vector C = 5j
∴Sum, A + B + C = 5i + 7.071(i + j) + 5j
= (5 + 7.071)i + (5 + 7.071)j
= 12.071(i +j)
Magnitude is always found by the Pythagoras theorem and the direction is given by θ = tan⁻¹ * (magnitude along y-axis/ magnitude along x-axis).
∴Magnitude of the resultant = √(12.071)²+(12.071)²
=√291.41
= 17.07
∴ Direction of the resultant, θ = tan⁻¹( 5 / 5 )
= tan⁻¹ (1)
= 45° or π/4 radians
