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.!