Question

ly Tulsel
3.
A vector of magnitude 10 has its rectangular components as 8 and 6 along x and y axes. Find
the angles it make with these axes.
1​

Answer 1

$\underline{\mathfrak{Answer:-}}$

Angle made by the vector with

x-axis = 37°

y-axis = 53°

$\underline{\mathfrak{Explanation:-}}$

Given

Magnitude of the vector [|r|] = 10

Rectangular components are-

8 along X-axis

6 along Y-axis

To Find

Angles made by the vector with axes

Solution

Let, the angle made by the vector with

X-axis = α

Y-axis = β

As we know,

$\boxed{ cosA=\dfrac{Adj. side}{Hypoteneuse} }$

cosα = $\dfrac{x}{|r|}$

cosα = $\dfrac{8}{10}$

cosα = $\dfrac{4}{5}$

$\boxed{\alpha = 37 \degree}$

cosβ = $\dfrac{y}{|r|}$

cosβ = $\dfrac{6}{10}$

cosβ = $\dfrac{3}{5}$

$\boxed{\beta = 53 \degree}$

(or)

$\boxed{ tanA=\dfrac{opp.side}{Adj. side} }$

tanα = $\dfrac{6}{8}$

tanα = $\dfrac{3}{4}$

$\boxed{\alpha = 37 \degree}$

tanβ = $\dfrac{8}{6}$

tanβ = $\dfrac{4}{3}$

$\boxed{\beta = 53 \degree}$

Hence, the angles made by the vector with X and Y axes are 37° and 57° respectively