For any vector a, the value of | a i|^2+| a j|^2+| a k|^2 is equal to: · questionr

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Question 344 of 379MediumMCQ

For any vector

\vec a

, the value of

|\vec a\times\hat i|^2+|\vec a\times\hat j|^2+|\vec a\times\hat k|^2

is equal to:

Solutions · 1

Official solution

Let

\vec a=x\hat i+y\hat j+z\hat k

. Then

\vec a\times\hat i=z\hat j-y\hat k

, so

|\vec a\times\hat i|^2=y^2+z^2

. Similarly

|\vec a\times\hat j|^2=x^2+z^2

and

|\vec a\times\hat k|^2=x^2+y^2

. \[\text{Sum} = 2(x^2+y^2+z^2)=2|\vec a|^2\]

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