Question

Two forces of 6 N and 8 N act at a point at an angke
of 90' with each other. Determine the magnitude and
direction of the resultant force by drawing a vector
diagram.​

Answer 1

Answer:-

Let the two vectors be' a ' and ' b ' whose magnitude are 8N and 6N respectively.

Let the two vectors be' a ' and ' b ' whose magnitude are 8N and 6N respectively. Their resultant be 'R'.

Magnitude of resultant

$r = \sqrt{ {a}^{2} } + {b}^{2} + 2ab \cos( \alpha )$

$r = \sqrt{ {a}^{2} } + {b}^{2}$

as cos90 degree is zero.

$r = \sqrt{ {6}^{2} } + {8}^{2}$

$r = \sqrt{36 + 64}$

$r = \sqrt{100}$

$r = 10 \: units$

so, the resultant has a magnitude of 10N.

Direction of resultant

$\tan( \beta ) = \frac{b \sin( \alpha ) }{a + b \cos( \alpha ) }$

alpha is the angle between the two vectors I.e. 90 degrees.

$\tan( \beta ) = \frac{6 \times 1}{8 + 0}$

$\tan( \beta ) = \frac{3}{2}$

$\beta = 56.3 \: degrees$

so,the direction is 56.3 degrees from 8N.

# refer to the attachment for vector diagram.