Let a¯ be vector parallel to line intersection of planes P1 and P2 through origin. If P1 is  parallel to the vectors 2j¯+3k¯ and 4j¯-3k¯ and P2 is parallel to j¯-k¯ and 3i¯+3j¯ , the  angle between a¯ and 2i¯+j¯-2k¯

Let n¯1,n¯2 be normal to planes P1&P2 respectively.  Then n1¯=2j¯+3k¯×4j¯−3k¯=−6i¯−12i¯=−18i¯and n2¯=(j¯-k¯)×(3i¯+3j¯)=-3k¯-3j¯+3i¯ ∴a¯=n1¯×n¯2=i¯j¯k¯-18003-3-3=54i¯j¯k¯100-111=54(0.i¯-j¯+k¯) Let θ be the angle between -j¯+k¯ and 2i¯+j¯-2k¯ then cosθ=0−1−22.3=12 So, θ=π4∴ Angle =π4