Косинус угла между векторами х(1,0,0) и у(0,1,0) равен

 скалярное произведение  a · b = <span>ax</span> · <span>bx</span> + <span>ay</span> · <span>by</span> + <span>az</span> · <span>bz</span><span> = 1 · 0 + 0 · 1 + 0 · 0 = 0 + 0 + 0 = 0
длины векторов
</span>|a| = √<span><span>ax</span>2 + <span>ay</span>2 + <span>az</span>2</span> = √<span>12 + 02 + 02</span> = √1 + 0 + 0 = √1 =  1
|b| = √<span><span>bx</span>2 + <span>by</span>2 + <span>bz</span>2</span> = √<span>02 + 12 + 02</span> = √0 + 1 + 0 = √1<span> =  1
</span>угол между векторами
<span><span><span>cos α = </span><span>a · b/</span></span><span>|a||b|
</span></span><span><span><span>cos α = </span>0<span> = 0/</span></span><span>1 ·  1

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