If a= i +6j+k and b= i+13j+k, how do you find a unit vector with positive first coordinate orthogonal to both a and b?

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Answer 1 · 2016-12-10T11:42:05

The unit vector is $=〈1/sqrt2,0,-1/sqrt2〉$

You have to do a cross product to find a vector perdendicular to $veca$ and $vecb$ .

The cross product is given by the determinant

$| (hati,hatj,hatk), (1,13,1), (1,6,1) |$

$=hati(13-6)-hatj(1-1)+hatk(6-13)$

$=〈7,0,-7〉$

Verification by doing the dot products

$〈7,0,-7〉.〈1,6,1〉=7-7=0$

$〈7,0,-7〉.〈1,13,1〉=7-7=0$

The unit vector is obtained by dividing withe the modulus

The modulus $=sqrt(49+49)=7sqrt2$

The unit vector $=1/(7sqrt2)〈7,0,-7〉$

$=〈1/sqrt2,0,-1/sqrt2〉$