The ratio in which the plane r→⋅$$(i$$→−$$2j$$→$$+3k$$→$$)=17$$ divides the line joining the points −$$2i$$→$$+4j$$→$$+7k$$→ and $$3i$$→−$$5j$$→$$+8k$$→ is

Question

The ratio in which the plane r→⋅$$(i$$→−$$2j$$→$$+3k$$→$$)=17$$ divides the line joining the points −$$2i$$→$$+4j$$→$$+7k$$→ and  $$3i$$→−$$5j$$→$$+8k$$→ is

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Let the plane r→⋅$$(i$$→−$$2j$$→$$+3k$$→$$)=17$$ divide the line joining  the points −$$2i$$→$$+4$$→j˙$$+7k$$→ and $$3i$$→−$$5j$$→$$+8k$$→ in the ratio t:$$1$$ at point PTherefore, point P is $$3t$$−$$2t+1i$$→$$+$$−$$5t+4t+1j$$→$$+8t+7t+1k$$→This lies on the given plane∴ $$3t$$−$$2t+1$$⋅$$(1)+$$−$$5t+4t+1($$−$$2)+8t+7t+1(3)=17Solving$$, we $$gett=310$$

$The ratio in which the plane \vec{r} \cdot (\vec{i} - 2 \vec{j} + 3 \vec{k}) = 17 divides the line joining the points - 2 \vec{i} + 4 \vec{j} + 7 \vec{k} and$ $3 \vec{i} - 5 \vec{j} + 8 \vec{k} is$

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The ratio in which the plane r→⋅(i→−2j→+3k→)=17 divides the line joining the points −2i→+4j→+7k→ and 3i→−5j→+8k→ is

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$The ratio in which the plane \vec{r} \cdot (\vec{i} - 2 \vec{j} + 3 \vec{k}) = 17 divides the line joining the points - 2 \vec{i} + 4 \vec{j} + 7 \vec{k} and$ $3 \vec{i} - 5 \vec{j} + 8 \vec{k} is$