What is the unit vector that is normal to the plane containing (i+k) and #(2i+ j - 3k)?

1 Answer
P dilip_k
May 27, 2016

±3ˆi−3ˆj+ˆk√19

Explanation:

If →A=ˆi+ˆjand→B=2ˆi+ˆj−3ˆk
then vectors which will be normal to the plane containing →Aand→B are either→A×→Bor→B×→A .So we are to find out the unit vectors of these two vector . One is opposite to another.

Now →A×→B=(ˆi+ˆj+0ˆk)×(2ˆi+ˆj−3ˆk)
=(1⋅(−3)−0⋅1)ˆi+(0⋅2−(−3)⋅1)ˆj+(1⋅1−1⋅2)ˆk
=−3ˆi+3ˆj−ˆk

So unit vector of →A×→B=→A×→B∣∣∣→A×→B∣∣∣
=−3ˆi−3ˆj+ˆk√32+32+12=−3ˆi−3ˆj+ˆk√19

And unit vector of →B×→A=+3ˆi−3ˆj+ˆk√19

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