Find the vectors, not with determinants, but by using properties of cross products. (i+j)\times(i-J) and k\times(i-2j)

a2linetagadaW

a2linetagadaW

Answered question

2021-05-04

Find the vectors, not with determinants, but by using properties of cross products.
(i+j)×(iJ)
and
k×(i2j)

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2021-05-05Added 108 answers

Step 1
(i+j)×(ij)
=i×ui×j+j×ij×j
=0kk0=2k
k×(i2j)=k×i2(k×j)=j2(i)=2i+j
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-06Added 2605 answers

The cross product has to be orthogonal to both i+j and i-j. Let v be this cross product. Then <i+j,v>=<i,v>+<j,v>=0 and <i-j,v>=<i,v>-<j,v>=0. What can you conclude?

Now that we know i and j are unit vectors, we can do a little better. If we write v=ai+bj+ck,

<i,v>=a, <j,v>=b

The last fact you'll need is that |v|=i||j||sinθ|=|sinθ|. Can you figure out what the angle between i+j and i-j is?

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