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AnnZ [28]
2 years ago
14

Which description of the vector shown is correct ?

Mathematics
2 answers:
BartSMP [9]2 years ago
8 0

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}.

So, the magnitude of the vector is 7\sqrt 2 which makes 135 ^{\circ} with the positive direction of the x-axis.

Hence, option (B) is correct.

irina [24]2 years ago
4 0

Answer:

B

Step-by-step explanation:

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