First slide

Algebra of vectors

Question

The adjacent sides of parallelogram are $\vec{a} = \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ . Hence the length of the longer diagonal of the parallelogram is

Moderate

A

1
B

4
C

2..26
D

7

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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