If A|B , A|C, B(2,3,2) , C(1,2,1) and NormA=4√(2) then A=...... ?

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Answer 1 · 2018-05-08T18:51:06

# vecA=(-4,0,4) or (4,0,-4)#.

I hope the Question is to find #vecA#, given that

#vecA bot vecB, vecA bot vecC, and ||vecA||=4sqrt2#.

Now, since, #vecA bot vecB and vecA bot vecC#,

#vecA# must be along #vecBxxvecC#.

So, let, #vecA=k(vecBxxvecC), k!=0#.

Now, #vecBxxvecC=|(i,j,k),(2,3,2),(1,2,1)|#,

#=(3-4)i-(2-2)j+(4-3)k#.

#:. vecA=k(vecBxxvecC)=(-k,0,k)#.

But, then, #||vecA||=sqrt{(-k)^2+0+k^2}=|k|sqrt2#.

Knowing that, #||vecA||=4sqrt2, |k|=4, or, k=+-4#.

#"Therefore, "vecA=(-4,0,4) or (4,0,-4)#.

Enjoy Maths.!