How do you find a unit vector that is orthogonal to a and b: a = 7 i − 4 j + 8 k and b = −7 i + 9 j + 4 k?

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Answer 1 · 2016-09-27T14:38:54

$"The reqd. unit vector"=-88/sqrt16025i-84/sqrt16025j+35/sqrt16025k$

$~~1/126.59(-88i-84j+35k)$

We know from Vector Geometry that the Vector or Outer

Product of $veca & vecb$ , i.e., $vecaxxvecb$ is orthogonal

to both of them.

The Unit Vector, then, is, $(vecaxxvecb)/||(vecaxxvecb)||$ .

Now, $vecaxxvecb=(7,-4,8)xx(-7,9,4)$

$=|(i,j,k),(7,-4,8),(-7,9,4)|$

$=(-16-72)i-(28+56)j+(63-28)k$

$=-88i-84j+35k$

$:. ||(vecaxxvecb)||=sqrt{(-88)^2+(-84)^2+35^2}$

$=sqrt(7744+7056+1225)=sqrt16025~~126.59$ .

Hence, the reqd. unit vector $=-88/sqrt16025i-84/sqrt16025j+35/sqrt16025k$

or, $~~1/126.59(-88i-84j+35k)$

Enjoy Maths.!