Question

Example 25 Find the angle between the line x + 1 2-3 = у 3 II 2 6 and the plane 10 x + 2y - 11 z = 3. Solution Let O be the angle between the line and the normal to the plane. Converting the given equations into vector form, we have 7 = (-i + 3 Ê ) + 2 (2 i + 3 h +6 h) and 7.(10 î +2 j - 11 h) = 3 Here b = 2 +3 ) +6k and n = 10 +2 -11 k - sin o = (2 i +3 h + 6k). (10 i + 2 } – 11 h) hi + 2 j - √2² V22 + 32 + 6 102 + 22 +112 + 40 -8 8 8 = | 8 7x15 21 21 or o = sin 21​

Answer 1

Let thetha be the angle between the line and the normal to the plane. Converting the given equations into vector form, we have