91Ó°ÊÓ

Find the magnitude of the vector a and the smallest positive angle \(\boldsymbol{\theta}\) from the positive \(\boldsymbol{x}\) -axis to the vector \(O P\) that corresponds to a. $$\mathbf{a}=2 \mathbf{i}-3 \mathbf{j}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-5-5 \sqrt{3} i$$

Exer. 35-40: Prove the property if a and b are vectors and \(m\) is a real number. $$\mathbf{a} \cdot \mathbf{b}=\mathbf{b} \cdot \mathbf{a}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-5-5 \sqrt{3} i$$

The vectors a and b represent two forces acting at the same point, and \(\boldsymbol{\theta}\) is the smallest positive angle between a and b. Approximate the magnitude of the resultant force. $$\|\mathbf{a}\|=40 \mathrm{lb}, \quad\|\mathbf{b}\|=70 \mathrm{lb}, \quad \theta=45^{\circ}$$

Exer. 35-40: Prove the property if a and b are vectors and \(m\) is a real number. $$(m a) \cdot \mathbf{b}=m(\mathbf{a} \cdot \mathbf{b})$$

Approximate the area of triangle \(A B C.\) \(\alpha=60^{\circ}, \quad b=20, \quad c=30\)

Exer. 35-40: Prove the property if a and b are vectors and \(m\) is a real number. $$m(\mathbf{a} \cdot \mathbf{b})=\mathbf{a} \cdot(m \mathbf{b})$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$\sqrt{3}-i$$

The vectors a and b represent two forces acting at the same point, and \(\boldsymbol{\theta}\) is the smallest positive angle between a and b. Approximate the magnitude of the resultant force. $$\|\mathbf{a}\|=5.5 \mathrm{lb}, \quad\|\mathbf{b}\|=6.2 \mathrm{lb}, \quad \theta=60^{\circ}$$