Answer
$\approx 417 N$
Work Step by Step
$| \tau|=|r \times f|= |r||f|sin \theta$
Given: $|r|=30 cm=0.30 m$;$r=30 j$,
$r \cdot \lt 0,3,-4 \gt =|r| (\sqrt {0+9+16}) cos \theta= (30) (5) cos \theta$
Hence, $90=150 cos \theta$
$ cos \theta=\frac{90}{150}=\frac{3}{5}$
$sin \theta=\sqrt {1-cos^2 \theta}=\sqrt {1-\frac{9}{25}}=\frac{4}{5}$
$| \tau|=|r \times f|= |r||f|sin \theta$
$ 100 N m=0.30 \cdot |f| \cdot \frac{4}{5}$
$ |f| =\frac{1250}{3} \approx 417 N$
