{"id":6368,"date":"2021-10-13T17:56:29","date_gmt":"2021-10-13T12:26:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6368"},"modified":"2022-01-16T17:05:17","modified_gmt":"2022-01-16T11:35:17","slug":"intercept-form-of-a-plane","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/intercept-form-of-a-plane\/","title":{"rendered":"Intercept Form of a Plane – Equation and Example"},"content":{"rendered":"

Here you will learn intercept form of a plane equation with examples.<\/p>\n

Let’s begin –<\/p>\n

Intercept Form of a Plane<\/h2>\n
\n

The equation of a plane intercepting lengths a, b and c with x-axis, y-axis and z-axis respectively is<\/p>\n

\\(x\\over a\\) + \\(y\\over b\\) + \\(z\\over c\\) = 1<\/p>\n<\/blockquote>\n

Note<\/strong> :<\/p>\n

1)<\/strong>. The above equation is known as the intercept form of the plane, because the plane intercepts length a, b and c with x, y and z-axes respectively.<\/p>\n

2)<\/strong>. To determine the intercepts made by a plane with the coordinate axes we proceed as follows :<\/p>\n

For x-intercept : Put y = 0, z = 0 in the equation of the plane and obtain the value of x. The value of x is the intercept on x-axis.<\/p>\n

For y-intercept : Put x = 0, z = 0 in the equation of the plane and obtain the value of y. The value of y is the intercept on y-axis.<\/p>\n

For z-intercept : Put x = 0, y = 0 in the equation of the plane and obtain the value of z. The value of z is the intercept on z-axis.<\/p>\n

Example<\/strong><\/span> : Write the equation of the plane whose intercepts on the coordinates axes are -4, 2 and 3 respectively.<\/p>\n

Solution<\/span><\/strong> : We know that the equation of a plane having a, b and c intercept on the coordinate axes is given by \\(x\\over a\\) + \\(y\\over b\\) + \\(z\\over c\\) = 1<\/p>\n

Here a = -4, b = 2, and c = 3. So ,the equation of the required plane is<\/p>\n

\\(x\\over -4\\) + \\(y\\over 2\\) + \\(z\\over 3\\) = 1 <\/p>\n

\\(\\implies\\)  -3x + 6y + 4z =12<\/p>\n\n\n

\n
Next – Equation of Plane in Vector form<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of Plane Passing Through Three Points<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn intercept form of a plane equation with examples. Let’s begin – Intercept Form of a Plane The equation of a plane intercepting lengths a, b and c with x-axis, y-axis and z-axis respectively is \\(x\\over a\\) + \\(y\\over b\\) + \\(z\\over c\\) = 1 Note : 1). The above equation is …<\/p>\n

Intercept Form of a Plane – Equation and Example<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[33],"tags":[],"yoast_head":"\nIntercept Form of a Plane - Equation and Example<\/title>\n<meta name=\"description\" content=\"In this post you will learn intercept form of a plane equation with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/intercept-form-of-a-plane\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Intercept Form of a Plane - 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