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If veca=5hati-hatj-3hatk and vecb=hati+3...

If `veca=5hati-hatj-3hatk` and `vecb=hati+3hatj-5hatk`, then show that the vectors `veca+vecb` and `veca-vecb` are perpendicular.

Text Solution

Verified by Experts

We know that two non-zero vectors are perpendiclar if their scalar product is zero.
Here `" " veca+vecb=6hati+2hatj-8hatk`
`veca-vecb=4ahti-4ahtj+2hatk`
SO, `" "(veca+vecb).(veca-vecb)=(6hati+2hatj-8hatk)(4hati-4hatj+2hatk)`
`=24-8-16=0`.
Hence `veca+vecb` and `veca-vecb` are perpendicular vectors.
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