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Lv 4
? asked in Science & MathematicsMathematics · 9 years ago

Find u x v and show that it is orthogonal to both u and v?

u= -3, 2, 3

v= 0, 1, 0

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    u x v=(u2v3-u3v2)i+(u3v1-u1v3)j+(u1v2-u2v1)k

    u x v=(2*0-3*1)i+(3*0-3*0)j+(-3*1-2*0)

    =(-3,0,-3)

    To show that u x v is orthogonal to u and v then the dot product of it with any of them is 0

    (u x v).u=(-3,0,-3).(-3, 2, 3)=9+0+-9=0

    (u x v).v=(-3,0,-3).(0, 1, 0)=0+0+0=0

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