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If ABCD is parallelogram, AB=2hati+4hatj...

If ABCD is parallelogram, `AB=2hati+4hatj-5hatk and AD=hati+2hatj+3hatk`, then the unit vectors in the direction of BD is

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The correct Answer is:
7
Vectors along to sides are `a=hati+2hatj+hatk and b=2hati+4hatj+hatk`
clearly the vector along the longer diagonal is
`a+b=3hati+6hatj+2hatk`
Hence, length of the longer diagonal is
`|a+b|=|3hati+6hatj+2hatk|=7`
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