Find a vector in the direction of a¯=i^-2j^ that has magnitude 7 units. - Mathematics and Statistics

Question

Find a vector in the direction of $\bar{a} = \hat{i} - 2 \hat{j}$ that has magnitude 7 units.

Sum

Solution

$\bar{a} = \hat{i} - 2 \hat{j}$

$∴ | \bar{a} | = \sqrt{1^{2} + {(- 2)}^{2}} = \sqrt{5}$

Unit vector in direction of $\bar{a} = \hat{a} = \frac{\bar{a}}{| \bar{a} |}$

= $\frac{\hat{i} - 2 \hat{j}}{\sqrt{5}}$

∴ Vector of magnitude 7 in the direction of $\bar{a} = 7 \hat{a}$

= $7 (\frac{\hat{i} - 2 \hat{j}}{\sqrt{5}})$

= $\frac{7}{\sqrt{5}} \hat{i} - \frac{14}{\sqrt{5}} \hat{j}$

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Vectors and Their Types

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Q 7.Q 6.Q 8.

Chapter 5: Vectors - Exercise 5.1 [Page 151]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

Chapter 5 Vectors
Exercise 5.1 | Q 7. | Page 151

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Find a vector in the direction of a¯=i^-2j^ that has magnitude 7 units. - Mathematics and Statistics

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