Write the sum of intercepts cut off by the plane on the three axes. - Wired Faculty

Integrals

Question

Write the sum of intercepts cut off by the plane $straight r with rightwards arrow on top. open parentheses 2 straight i with hat on top plus straight j with hat on top minus straight k with hat on top close parentheses minus 5 space equals 0$ on the three axes.

Solution

Given,
$straight r with rightwards arrow on top. open parentheses 2 straight i with hat on top plus straight j with hat on top minus straight k with hat on top close parentheses minus 5 equals 0 in space cartesian space form 2 straight x space plus straight y minus straight z minus 5 space equals 0 2 straight x plus straight y minus straight z equals 5 fraction numerator 2 straight x over denominator 5 end fraction plus straight y over 5 minus straight z over 5 equals 1 fraction numerator straight x over denominator 5 divided by 2 end fraction plus straight y over 5 plus fraction numerator straight z over denominator negative 5 end fraction equals 1 Intercept space cutt space of space on space the space axes space open parentheses 5 over 2 comma 5 comma negative 5 close parentheses straight x over straight a plus straight y over straight b plus straight z over straight c equals 1 straight a equals 5 over 2 space straight b equals 5 space straight c equals negative 5 straight a plus straight b plus straight c equals 5 divided by 2$

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Integrals

Write the sum of intercepts cut off by the plane $straight r with rightwards arrow on top. open parentheses 2 straight i with hat on top plus straight j with hat on top minus straight k with hat on top close parentheses minus 5 space equals 0$ on the three axes.

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