Question

If ⃗ is the vector sum of ⃗ and ⃗⃗, ⃗ = ⃗ + ⃗⃗, what must be true about the directions and magnitudes of ⃗ and ⃗⃗ if = + ? What must be true about the directions and magnitudes of ⃗ and ⃗⃗ if = 0?

Answer 1

The magnitude of the vector sum of 2x and 3y is determined as 3.6 units and the direction is 56.3⁰.

Magnitude of the vector

The magnitude of two vectors is determined using the following formula;

$|V| = \sqrt{V_x^2 + V_y^2}$

Let the sum of the vector = 2x + 3y

The magnitude of the vectors is calculated as follows;

$|V| = \sqrt{2^2 + 3^2} \\\\|V| = 3.6 \ units$

Direction of the vectors

The direction of the vectors is calculated as follows;

$tan(\theta) = \frac{V_y}{V_x} \\\\tan(\theta) = \frac{3}{2} \\\\tan(\theta) = 1.5\\\\\theta = tan^{-1} (1.5)\\\\\theta = 56.3 \ ^0$

Thus, the magnitude of the vector sum of 2x and 3y is determined as 3.6 units and the direction is 56.3⁰.

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