Vectors along the adjacent sides of parallelogram are a→$$=i^+2j^+k^$$ and b→$$=2i^+4j^+k^$$ Find the length of the longer diagonal of the parallelogram'

Vectors along the sides are a→$$=i^+2j^+k^$$ and b→$$=2i^+4j^+k^Clearly$$ the vector along the longer diagonal is a→$$+b$$→$$=3i^+6j^+2k^Hence$$, length of the longer diagonal is|a→$$+b$$→|$$=$$|$$3i^+6j^+2k^$$|$$=7$$

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Vectors along the adjacent sides of parallelogram are $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ Find the length of the longer diagonal of the parallelogram'

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Solution

Vectors along the sides are $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k}$ and $\vec{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$
Clearly the vector along the longer diagonal is $\vec{a} + \vec{b} = 3 \hat{i} + 6 \hat{j} + 2 \hat{k}$
Hence, length of the longer diagonal is
$| \vec{a} + \vec{b} | = | 3 \hat{i} + 6 \hat{j} + 2 \hat{k} | = 7$

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Algebra of vectors

Remember concepts with our Masterclasses.

Vectors along the adjacent sides of parallelogram are a→=i^+2j^+k^ and b→=2i^+4j^+k^ Find the length of the longer diagonal of the parallelogram'

Vectors along the sides are a→=i^+2j^+k^ and b→=2i^+4j^+k^Clearly the vector along the longer diagonal is a→+b→=3i^+6j^+2k^Hence, length of the longer diagonal is|a→+b→|=|3i^+6j^+2k^|=7

Ready to Test Your Skills?

free study material

Vectors along the adjacent sides of parallelogram are $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ Find the length of the longer diagonal of the parallelogram'