How do you find two unit vectors orthogonal to both i-j+k and 4j+4k?

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Answer 1 · 2017-03-05T14:17:10

$+-1/sqrt6(-2,-1,1).$

Let us recall that, for vectors $veca and vecb$ , their Vector

(Cross) Product , i.e., $veca xx vecb$ is Orthogonal to both

$vec a and vec b.$

The Desired Unit Vectors, then, can be obtained by,

$+-(vecaxxvecb)/||(vecaxxvecb)||$ .

Now, with $veca=i-j+k=(1,-1,1), &, vecb=4j+4k=4(0,1,1)$ , we have,

$veca xx vecb=|(i,j,k),(1,-1,1),(0,4,4)|=4|(i,j,k),(1,-1,1),(0,1,1)|$

$=4(-2,-1,1)$ ,

$rArr ||(vecaxxvecb)||=4sqrt{(-2)^2+(-1)^1+1^2}=4sqrt6.$

Hence, the desired vectors are, $(+-4(-2,-1,1))/(4sqrt6), or,$

$+-1/sqrt6(-2,-1,1).$

Enjoy Maths.!