Question

A unit vector perpendicular to a =2i^+3j^+k^ and b =i^j^+k^ both is

Answer 1

Answer:

Step-by-step explanation:

We know that cross product of any two vectors yields a vector which is perpendicular to both vectors

∴ for two vectors →Aand→B if →C is the vector perpendicular to both.

→C=→A×→B=⎡⎢⎣ˆiˆjˆkA1A2A3B1B2B3⎤⎥⎦

=(A2B3−B2A3)ˆi−(A1B3−B1A3)ˆj+(A1B2−B1A2)ˆk.

Inserting given vectors we obtain

→C=⎡⎢⎣ˆiˆjˆk2111−12⎤⎥⎦

=(1×2−(−1)×1)ˆi−(2×2−1×1)ˆj+(2×(−1)−1×1)ˆk.

=3ˆi−3ˆj−3ˆk.

Now unit vector in the direction of →C is →C∣∣∣→C∣∣∣

∴∣∣∣→C∣∣∣=√32+(−3)2+(−3)2

=√27

=3√3

Therefore desired unit vector is

1√3(ˆi−ˆj−ˆk)

Answer 2

Answer:

Step-by-step explanation:

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