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Given à = √2 â – 3 ŷ and B = −2+√3 ŷ. Which of the following(s) is (are) true? (a) A + B is parallel to the z-axis. (b) (‡Ã+ Â) · ŷ = (c) Â=√√√√9 (d) Vector C = -6 2-6 ŷ is 105° counterclockwise from vector B. (e) Vector D = √3+3 ŷ is perpendicular to vector B.

Given à = √2 â – 3 ŷ and B = −2+√3 ŷ. Which of the following(s) is (are) true? (a) A + B is parallel to the z-axis. (b) (‡Ã+ Â) · ŷ = (c) Â=√√√√9 (d) Vector C = -6 2-6 ŷ is 105° counterclockwise from vector B. (e) Vector D = √3+3 ŷ is perpendicular to vector B.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given \(\vec{A} = \sqrt{2} \hat{x} - 3 \hat{y}\) and \(\vec{B} = -\hat{x} + \sqrt{3} \hat{y}\). Which of the following(s) is(are) true? (a) \(\frac{1}{\sqrt{2}} \vec{A} + \vec{B}\) is parallel to the x-axis. (b) \(\left( \frac{1}{\sqrt{2}} \vec{A} + \vec{B} \right) \cdot \hat{y} = 0\) (c) \(\vec{A} = \sqrt{\frac{2}{11}} \hat{x} - \sqrt{\frac{9}{11}} \hat{y}\) (d) Vector \(\vec{C} = -6 \hat{x} - 6 \hat{y}\) is 105° counterclockwise from vector \(\vec{B}\). (e) Vector \(\vec{D} = \sqrt{3} \hat{x} + 3 \hat{y}\) is perpendicular to vector \(\vec{B}\). Explanation of Graphs or Diagrams: - The image contains a mathematical problem involving vectors and their properties. - There are no diagrams or graphs included in the image.
Transcribed Image Text:Given \(\vec{A} = \sqrt{2} \hat{x} - 3 \hat{y}\) and \(\vec{B} = -\hat{x} + \sqrt{3} \hat{y}\). Which of the following(s) is(are) true? (a) \(\frac{1}{\sqrt{2}} \vec{A} + \vec{B}\) is parallel to the x-axis. (b) \(\left( \frac{1}{\sqrt{2}} \vec{A} + \vec{B} \right) \cdot \hat{y} = 0\) (c) \(\vec{A} = \sqrt{\frac{2}{11}} \hat{x} - \sqrt{\frac{9}{11}} \hat{y}\) (d) Vector \(\vec{C} = -6 \hat{x} - 6 \hat{y}\) is 105° counterclockwise from vector \(\vec{B}\). (e) Vector \(\vec{D} = \sqrt{3} \hat{x} + 3 \hat{y}\) is perpendicular to vector \(\vec{B}\). Explanation of Graphs or Diagrams: - The image contains a mathematical problem involving vectors and their properties. - There are no diagrams or graphs included in the image.
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