Trong không gian tọa độ cho đường thẳng có phương trình và mặt phẳng có phương trình . Tính của góc tạo bởi đường thẳng và mặt phẳng .

Giải thích

Đường thẳng có , mặt phẳng có . sin α , ∆ = 2 . 1 + - 1 . 1 + 2 . - 1 2 2 + 1 2 + 2 2 1 2 + 1 2 + 1 2 = 1 3 3 = 3 9 " src="https://img-question-vn.ruangguru.com/WRR3u4ysIuI9O3wOe6ScaGoxVrT0mxDtq3oSh_-DHWz3cFup3NEmBwkYxo0NtZbrXwZL4nojIn01vHCoQvs8jIMRSGDTEmUrQoSGV1hQ4U-z5goBigX28LH5-mxiKeE8HJ85XTwX" style="width: 272.00px; height: 108.00px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="sin open parentheses open parentheses alpha close parentheses comma increment close parentheses equals fraction numerator open vertical bar 2.1 plus negative 1.1 plus 2. negative 1 close vertical bar over denominator square root of 2 squared plus 1 squared plus 2 squared end root square root of 1 squared plus 1 squared plus 1 squared end root end fraction equals fraction numerator 1 over denominator 3 square root of 3 end fraction equals fraction numerator square root of 3 over denominator 9 end fraction"> ⇒ cos α , ∆ = 1 - sin 2 α , ∆ = 1 - 3 9 2 = 78 9 " src="https://img-question-vn.ruangguru.com/ro3rGpfbO86MzLvfHcOjdbMhAOkJA-Zl8mQ1DdjbBAzq39IlhWdZuFNYapF75Nt_LhHKc8UsnV30KXp3uYlLChlPWubIYHVWKPyLBlOpTxZVc4ZUZ9rnij1xF-wwoUSE0LHZ7qf8" style="width: 220.00px; height: 85.33px; margin-left: 0.00px; margin-top: 0.00px; transform: rotate(0.00rad) translateZ(0px); -webkit-transform: rotate(0.00rad) translateZ(0px);" title="rightwards double arrow cos open parentheses open parentheses alpha close parentheses comma increment close parentheses equals square root of 1 minus sin squared open parentheses open parentheses alpha close parentheses comma increment close parentheses end root equals square root of 1 minus open parentheses fraction numerator square root of 3 over denominator 9 end fraction close parentheses squared end root equals fraction numerator square root of 78 over denominator 9 end fraction"> .