Question

.if vector A lies in third quadrant the direction will be : a) 180- b) 360- c) 180+ d) None

Answer 1

Answer:

(c)180+

Explanation:

You can also see that this vector lies in the third quadrant; the direction angle is between 180o and 270o.

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Answer 2

Answer:

Explanation:

A vector is defined by its magnitude and the direction.

Magnitude of a vector is the numerical value associated with the vector in a particular direction.

The direction of a vector is defined by its orientation with respect to the x-axis.

A vector is indicated by a line with an arrow on the top and a fixed point at the other end.

The direction of a vector is defined by the rotation of vector in counter clockwise direction about its tail due east from the origin.

The direction of a vector is denoted by

$\vec A=|A|\hat A$

where $|A|$ is the magnitude and $\hat A$  is a unit vector and denotes the direction of the vector A.

Let a two dimensional vector be

$\vec A=a_x\hat i+a_y\hat j$

In third quadrant, both the x- and y- coordinates are negative and the angle lies between 180° to 270°.

The angle of the vector is given by

$\theta=tan^{-1}\dfrac{y}{x}=tan^{-1}\dfrac{a_y}{a_x}$

Then the direction angle is given by $\theta_A=180^{o}+ \theta$.

So, the correct answer is option C.

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