The altitude of parallelopiped whose three coterminous edges are the vectors, A→$$=i^+j^+k^$$;B→$$=2i^+4j^$$−$$k^$$ and C→$$=i^+j^+3k^$$ with A→ and B→ as the sides of the base of the parallelopipied, is

Question

The altitude of parallelopiped whose three coterminous edges are the vectors, A→$$=i^+j^+k^$$;B→$$=2i^+4j^$$−$$k^$$ and C→$$=i^+j^+3k^$$ with A→ and B→ as the sides of  the base of the parallelopipied, is

Infinity Learn · Accepted Answer

h  $$=$$  A→ B→ C→|A→  ×B→|  and  | A→  ×B→|   $$=$$   a→$$2$$ b→$$2$$ − $$(a$$→ ⋅ b→$$)2a$$→$$2$$ b→$$2$$ − $$(a$$→ ⋅ b→$$)2=3$$ ×$$21-(2+4-1)2=63-25=38A$$→ × B→$$=$$ $$-5i^+3j^+2k^A$$→ B→ C→$$=A$$→ × B→.C→$$=-5i^+3j^+2k^$$· $$i^+j^+3k^=4$$∴$$h=438=43838=23819$$

$The altitude of parallelopiped whose three coterminous edges are the vectors,$ $\vec{A} = \hat{i} + \hat{j} + \hat{k}; \vec{B} = 2 \hat{i} + 4 \hat{j} - \hat{k} and \vec{C} = \hat{i} + \hat{j} + 3 \hat{k} with \vec{A} and \vec{B} as the sides of$ $the base of the parallelopipied, is$

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The altitude of parallelopiped whose three coterminous edges are the vectors, A→=i^+j^+k^;B→=2i^+4j^−k^ and C→=i^+j^+3k^ with A→ and B→ as the sides of the base of the parallelopipied, is

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$The altitude of parallelopiped whose three coterminous edges are the vectors,$ $\vec{A} = \hat{i} + \hat{j} + \hat{k}; \vec{B} = 2 \hat{i} + 4 \hat{j} - \hat{k} and \vec{C} = \hat{i} + \hat{j} + 3 \hat{k} with \vec{A} and \vec{B} as the sides of$ $the base of the parallelopipied, is$