From simple queries to complex problems, IDNLearn.com provides reliable answers. Discover in-depth answers to your questions from our community of experienced professionals.
Sagot :
The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
What do we mean by a vector?
- Vector is a colloquial term in mathematics and physics that refers to some quantities that cannot be expressed by a single number (a scalar) or to elements of some vector spaces.
- Vectors were first used in geometry and physics (typically in mechanics) to represent quantities with both a magnitude and a direction, such as displacements, forces, and velocity.
- In the same way that distances, masses, and time are represented by real numbers, such quantities are represented by geometric vectors.
To find the angle of the given vector:
Given: [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]
So,
[tex]\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}[/tex]
Using the formula [tex]\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}[/tex], we obtain:
[tex]\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}[/tex]
Therefore, the angle that the vector [tex]\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is (B) tan⁻¹ 2/3.
Know more about a vector here:
https://brainly.com/question/25705666
#SPJ4
The correct question is given below:
The angle that the vector [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex] makes with the y-axis is:
(A) tan⁻¹ 3/2
(B) tan⁻¹ 2/3
(C) sin⁻¹ 2/3
(D) cos⁻¹ 3/2
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.
