\( \left\{\begin{array}{l}\text { 3. Decidir, justificando adecuadamente, si las siguientes proposiciones son } \mathrm{V} \text { o } \mathrm{F} \text { : } \\ \text { a) El plano: } \pi:(x ; y ; z)=\alpha(1 ; 0 ;-1)+\beta(0 ; 1 ; 2)+(0 ; 0 ; 2) \text { y la recta } r:(x ; y ; z)=\lambda(2 ; 1 ; 0)+ \\ (2 ; 1 ; 2) \text { son perpendiculares. } \\ \text { b) Dados dos vectores perpendiculares } \vec{u} \text { y } \vec{w} \text {, se sabe que satisfacen: }\|\vec{w}\|=2\|\vec{u}\| \text {, entonces } \\ (3 \vec{u}+3 \vec{w}) \cdot(-\vec{w}+4 \vec{u})=0\end{array}\right. \)

ai The sides of a big triangle measure 100 m each. The sides of a small triangic measure 10 m less than the sides of the big triangle. fipd the perimeter of the big triangle. (ii) Find the perimeter of the smail trian is the ditference between the two perimeters?

Homework 1. find the crea of a rectangler with langth 6 cm and breadth \( \frac{12}{2} \mathrm{~cm} \)

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: \( \square \mathrm{cm} \) Length of the longer leg: \( \square \mathrm{cm} \) Length of the hypotenuse: \( \square \mathrm{cm} \)

The diameter of a circle measures 20 ft. What is the circumference of the circle?Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

In this exercise, lines m and n are parallel. Find the measure of each numbered angle.