Let \( P_{1}: 2 x+y-z=3 \) and \( P_{2}: x+2 y+z=2 \) be two planes. Then, which of the followin.... VIDEO
Let \( P_{1}: 2 x+y-z=3 \) and \( P_{2}: x+2 y+z=2 \) be two planes. Then, which of the following statement(s) is(are) TRUE?
(1) The line of intersecting of \( P_{1} \) and \( P_{2} \) has direction ratios, \( 1,2,-1 \)
(2) The line \( \frac{3 x-4}{9}=\frac{1-3 y}{9}=\frac{z}{3} \) is perpendicular to the line of intersection of \( P_{1} \) and \( P_{2} \)
(3) The acute angle between \( P_{1} \) and \( P_{2} \) is \( 60^{\circ} \)
(4) If \( P_{3} \) is the plane passing through the point \( (4,2,-2) \) and perpendicular to the line of intersection of \( P_{1} \) and \( P_{2} \), then the distance of the point \( (2,1,1) \) from the plane \( P_{2} \) is \( \frac{2}{\sqrt{3}} \)
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