The altitude of a parallelepiped whose three coterminous edges are vectors a¯$$=i$$¯$$+j$$¯$$+k$$¯,b¯$$=2i$$¯$$+4j$$¯−k¯ and c¯$$=i$$¯$$+j$$¯$$+3k$$¯ with a¯ and b¯ as sides of the base of the parallelopiped is

Question

The altitude of a parallelepiped whose three coterminous edges are vectors a¯$$=i$$¯$$+j$$¯$$+k$$¯,b¯$$=2i$$¯$$+4j$$¯−k¯ and c¯$$=i$$¯$$+j$$¯$$+3k$$¯ with a¯ and b¯ as sides of the base of the parallelopiped is

Infinity Learn · Accepted Answer

Let a→$$=i^+j^+k^$$         b→$$=2i^+4j^-k^$$        c→$$=i^+j^+3k^$$    volume of parallelopiped is a¯ b¯ c¯ $$=11124-1113=4$$ base area whose sides are a¯,b¯ is $$=a$$×$$b=ijk11124-1$$                                                     $$=38$$   height of $$parallelopiped=$$ volume base $$area=438=$$

$The altitude of a parallelepiped whose three coterminous edges are vectors$ $\bar{a} = \bar{i} + \bar{j} + \bar{k}, \bar{b} = 2 \bar{i} + 4 \bar{j} - \bar{k} and \bar{c} = \bar{i} + \bar{j} + 3 \bar{k} with \bar{a} and \bar{b} as sides of the base of the$ $parallelopiped is$

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The altitude of a parallelepiped whose three coterminous edges are vectors a¯=i¯+j¯+k¯,b¯=2i¯+4j¯−k¯ and c¯=i¯+j¯+3k¯ with a¯ and b¯ as sides of the base of the parallelopiped is

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$The altitude of a parallelepiped whose three coterminous edges are vectors$ $\bar{a} = \bar{i} + \bar{j} + \bar{k}, \bar{b} = 2 \bar{i} + 4 \bar{j} - \bar{k} and \bar{c} = \bar{i} + \bar{j} + 3 \bar{k} with \bar{a} and \bar{b} as sides of the base of the$ $parallelopiped is$