YZ=10, the whole circle os 154 degrees

Mathematics

1 answer:

AlladinOne [14]2 years ago

8 0

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Which description of the vector shown is correct ?

BartSMP [9]

Answer:

(B) The magnitude is 7sqrt2, and the direction angle is approximately 135 degrees.

Step-by-step explanation:

From the figure, the coordinate of the tail of the vector,

$(x_1,y_1)=(3,-6).$

The coordinate of the head of the vector,

$(x_2,y_2)=(-4,1).$

The magnitude of a vector is the length between the head and tail of the vector.

By using the distance formula,

the magnitude of the vector $= \sqrt{(1-(-6))^2+(-4-3)^2}$

$=\sqrt{(7^2+(-7)^2}\\\\=\sqrt{98}\\\\=7\sqrt{2}$

Now, let $\theta$ be the angle made by the vector with the positive direction of the x-axis, so

$\tan\theta = \frac{y_2-y_1}{x_2-x_1}\\\\\Rightarrow \tan\theta = \frac{1-(-6)}{-4-3}=\frac{7}{-7}=-1 \\\\\Rightarrow \theta = \tan^{-1}(-1) \\\\\Rightarrow \theta =\pi- \tan^{-1}1 \\\\\Rightarrow \theta = \pi-\frac{\pi}{4} \\\\\Rightarrow \theta =\frac{3\pi}{4} \\\\\Rightarrow \theta = 135 ^{\circ}.$