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〉#