{"id":37060,"date":"2022-12-01T10:38:35","date_gmt":"2022-12-01T05:08:35","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=37060"},"modified":"2022-12-01T10:38:35","modified_gmt":"2022-12-01T05:08:35","slug":"ts-inter-1st-year-maths-1b-the-plane-formulas","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-maths-1b-the-plane-formulas\/","title":{"rendered":"TS Inter 1st Year Maths 1B The Plane Formulas"},"content":{"rendered":"
Learning these TS Inter 1st Year Maths 1B Formulas<\/a> Chapter 7 The Plane will help students to solve mathematical problems quickly.<\/p>\n \u2192 A plane is a proper subset of R’* which has atleast three non-collinear points and is such that for any two points in it. the line joining them also lies in it.<\/p>\n \u2192 The general equation of a plane in the first degree equation in x, y, z given by ax + by + cz + d = 0. the coefficients a, b, c represent direction ratios of normal to the plane.<\/p>\n \u2192 The equation of a plane passing through (x1<\/sub>, y1<\/sub>, z1<\/sub>) and perpendicular to the line with direction ratios a, b, c is a (x – x1<\/sub>) + b (y – y1<\/sub>) + c (z – z1<\/sub>) = 0.<\/p>\n \u2192 Normal form of the plane is lx + my + nz – p where \/. rn. n are direction cosine’s of normal and p is the perpendicular distance from origin to the plane.<\/p>\n \u2192 The perpendicular distance from (0, 0, 0) to ax + by + cz t d = 0 is \\(\\frac{|d|}{\\sqrt{a^2+b^2+c^2}\\)<\/p>\n \u2192 The perpendicular distance from A (x1<\/sub>, y1<\/sub>, z1<\/sub>) to the plane ax + by + cz + d = 0 is \\(\\frac{\\left|a x_1+b y_1+c z_1+d\\right|}{\\sqrt{a^2+b^2+c^2}}\\)<\/p>\n <\/p>\n \u2192 The distance between parallel planes ax + by + cz + d1<\/sub> = 0 and ax + by + cz + d2<\/sub> = 0 is \\(\\frac{\\left|d_1-d_2\\right|}{\\sqrt{a^2+b^2+c^2}}\\)<\/p>\n \u2192 The equation of plane with x. y. z intercepts a. b. c is \\(\\frac{x}{a}+\\frac{y}{b}+\\frac{z}{c}\\) = 1.<\/p>\n \u2192 The equation of the plane passing through 3 non-collinear points A (x1<\/sub>, y1<\/sub> z1<\/sub>). B (x2<\/sub>, y2<\/sub>, z2<\/sub>) and C (x3<\/sub>, y3<\/sub> z3<\/sub>) is \\(\\left|\\begin{array}{ccc} \u2192 If \u03b8 is the angle between planes a1<\/sub>x + b1<\/sub>y + c1<\/sub>z – d1<\/sub> = 0 and a2<\/sub>x + b2<\/sub>y + c2<\/sub>z + d2<\/sub> = 0 then cos \u03b8 = \\(\\)<\/p>\n \u2192 The planes a1<\/sub>x + b1<\/sub>y + c1<\/sub>z + d1<\/sub> = 0 and a2<\/sub>x + b2<\/sub>y – c2<\/sub>z + d = 0 are parallel if \\(\\frac{a_1}{a_2}=\\frac{b_1}{b_2}=\\frac{c_1}{c_2}\\) and perpendicular if a1<\/sub>a2<\/sub> + b1<\/sub>b2<\/sub> + c1<\/sub>c2<\/sub> = 0.<\/p>\n","protected":false},"excerpt":{"rendered":" Learning these TS Inter 1st Year Maths 1B Formulas Chapter 7 The Plane will help students to solve mathematical problems quickly. TS Inter 1st Year Maths 1B The Plane Formulas \u2192 A plane is a proper subset of R’* which has atleast three non-collinear points and is such that for any two points in it. … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[],"yoast_head":"\nTS Inter 1st Year Maths 1B The Plane Formulas<\/h2>\n
\nx-x_1 & y-y_1 & z-z_1 \\\\
\nx_2-x_1 & y_2-y_1 & z_2-z_1 \\\\
\nx_3-x_1 & y_3-y_1 & z_3-z_1
\n\\end{array}\\right|\\) = 0<\/p>\n