Question

Angle made by the resultant of two vectors p=3i+2j and q=2i+3j with positive y-axis

Answer 1

Answer:

45°

Explanation:

As the resultant is 5i+5j

tan=5/5

tan=1

Angle=45

With x axis and with y axis angle=90-45

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Answer 2

The measure of angle made by the resultant angle with positive y-axis is 45⁰.

Given:

P=3i+2j  

Q=2i+3j

To find:

The measure of angle made by the resultant angle with positive y-axis.

Solution:

• A vector is a quantity which has both direction and magnitude. Vectors are used to find direction and magnitude of a point in space.
• It is written in the form of A= ai+bj+ck where i is the x component, j is the y component and k is the z component.
• Magnitude of a vector is the length of the vector which can be determined using the formula:
• |A|= $\sqrt{a^{2} + b^{2} + c^{2} }$     (For A= ai+bj+ck)
• Resultant of a vector is defined as the sum of two vectors which has its own magnitude and direction.

Resultant angle =R= P+Q

R= 3i+2j + 2i+3j

R= (3+2) i + (2+3) j

R= 5i + 5j

|R|= $\sqrt{5^{2} + 5^{2}}$

|R|= $\sqrt{25+25}$

|R|= $\sqrt{50}$

|R|= 5√2

Let θ be the angle between the resultant angle with positive y-axis.

We can find the value of θ using the formula:

tanθ= $\frac{x}{y}$

tanθ= $\frac{5}{5}$

tanθ= 1

θ= tan⁻¹ (1)

θ= 45⁰

Therefore, the measure of angle made by the resultant angle with positive y-axis is 45⁰.

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