Question

Find the magnitude of the vector a and the smallest positive angle θ from the positive x-axis to the vector OP that corresponds to a. a=0,-5.

Answer 1

Answer:

|a| = 5

θ = 90°

Step-by-step explanation:

The position vector of a is OP.

$\vec{a}=<0,-5>$

The magnitude of a vector is square root of of sum of square of x and y component.

x-component of vector a = 0

y-component of vector b = -5

$|a|=\sqrt{0^2+(-5)^2}$

$|a|=\sqrt{25}$

$|a|=5$

The smallest positive angle θ from the positive x-axis to the vector OP

$\theta = \tan^{-1}\dfrac{\text{y-component}}{\text{x-component}}$

$\theta=\tan^{-1}(\dfrac{-5}{0})$

$\theta=\tan^{-1}(-\infty)$

$\theta=270^\circ\text{ and }-90^\circ$

Smallest possible angle is 90° with positive direction of x-axis.

Hence, the magnitude of vector a is 5 and smallest possible angle is 90°