Learning these TS Inter 1st Year Maths 1B Formulas Chapter 5 Three Dimensional Coordinates will help students to solve mathematical problems quickly.
TS Inter 1st Year Maths 1B Three Dimensional Coordinates Formulas
→ Perpendicular distances front the point P(x, y, z ) to yz, zx and xy planes are |x|, |y|, |z|.
→ The distance between points A (x1, y1, z1), B (x2, y2, z2) is AB = \(\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}\)
→ The coordinates of a point which divides A = (x1, y1, z1) and B = (x2, y2, z2) internally in the ratio m1 m2 is = \(\left(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}, \frac{m_1 z_2+m_2 z_1}{m_1+m_2}\right)\)
→ Coordinates of midpoint of a line segment AB joining
A = (x1, y1, z1) and B = (x2, y2, z2) is = \(\left(\frac{\mathrm{x}_1+\mathrm{x}_2}{2}, \frac{\mathrm{y}_1+\mathrm{y}_2}{2}, \frac{\mathrm{z}_1+\mathrm{z}_2}{2}\right)\).
→ The centroid of the triangle formed by the points A (x1, y1, z1) , B (x2, y2, z2), C(x3, y3, z3) is
G = \(\left(\frac{\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3}{3}, \frac{\mathrm{y}_1+\mathrm{y}_2+\mathrm{y}_3}{3}, \frac{\mathrm{z}_1+\mathrm{z}_2+\mathrm{z}_3}{3}\right)\)
→ The centroid of the tetrahedron formed by (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) is
G = \(\left(\frac{x_1+x_2+x_3+x_4}{4}, \frac{y_1+y_2+y_3+y_4}{4}, \frac{z_1+z_2+z_3+z_4}{4}\right)\)