Question

11. Find the rectangular components of a vector Ã, 15 unit
long when it form an angle with respect to +ve x-axis of (1) 50°,
(1) 130° (ill) 230°, (iv) 310°​

Answer 1

Answer:

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Explanation:

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Answer 2

Given:

The magnitude of vector à = 15 units

To Find:

Rectangular components of vector  Ã when it makes the following angles with x-axis:

(1) 50°,

(2) 130°

(3) 230°

(4) 310°​

Solution:

• Rectangular components of a vector are expressed as :

            Ã = AcosФ iˆ + AsinФ jˆ

where Ф is the angle made by a vector from the x-axis.

• Using this property we will solve for all parts.

(1) Ф = 50°

Components of vector = Acos50° iˆ +Asin50°jˆ

                                    ⇒ 0.642 Aiˆ + 0.766Ajˆ

                                   ⇒ 9.63 i^ + 11.49j^

(2) Ф = 130°

Components of vector = Acos130° iˆ +Asin130°jˆ

                                       ⇒ -0.642Aiˆ + 0.766Ajˆ

                                     ⇒ -9.63i^ + 11.49j^

(3) Ф =230°

Components of vector = Acos230 iˆ +Asin230°jˆ

                                  ⇒ -0.642Aiˆ -0.766Ajˆ  

                                  ⇒ -9.63i^ - 11.49j^  

                   

(4) Ф = 310°

Components of vector = Acos310° iˆ +Asin310°jˆ

                                    ⇒ 0.642Aiˆ -0.766Ajˆ

                                   ⇒ 9.63i^ -11.49j^

Thus rectangular components of vector  Ã is:

(1) 9.63 i^ + 11.49j^

(2) -9.63i^ + 11.49j^

(3) -9.63i^ - 11.49j^  

(4) 9.63i^ -11.49j^