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Find a unit vector perpendicular to eac...

Find a unit vector perpendicular to each of the vector ` veca+ vecb`and ` veca- vecb` where ` vec a=3 hat i+2 hat j+2 hat k` and ` vec b= hat i+2 hat j-2 hat k`

Text Solution

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Step 1: Find the cross product of a⃗ and b⃗ .
a^×b^ is the determinant of the matrix
`i^11j^−22k^3−1` a^×b^ =∣∣∣∣∣i^11j^−22k^3−1∣∣∣∣∣`
`⇒i^(2−6)−j^(−1−3)+k^(2+2)`
`⇒i^(−4)−j^(−4)+k^(4)`
`⇒−4i^+4j^+4k^`
Let `c⃗ =a^×b^`
Step 2: Find the unit vector
`c^: ...
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