Find a Cartesian equation for the curve and identify it: r²sin2θ = 1.
OR
2. Let vectors A = (2, 1, 3), B = (-5, 2, 1), and C = (2, 1, 1). Find the volume of the parallelepiped defined by vectors A, B, and C by calculating A ● (B x C) using the dot and cross product rules.
Answer to #2:
i j k
(-5) 2 1
2 1 1
= 2 1 i
1 1 i
= 5 1 j
2 1 j
= (-5) 2 k
2 1 k
= (2×1-1×1)i- (5×1-2×1)j + ((-5) ×1-2×2)k
=1i
=3j
=(-9)k
=(1,3,(-9)) =b×c
=(2,1,3)×(1,3,9)
=(2×1)+(1×3)+(3×(-9))
=2+3+(-27)
=(-22)
v=/-22\
=22
