If f(x) = x + 7 and g(x) = x – 7, x ∈ R, find (fog) (7)
Evaluate: sinπ3 - sin-1 12
Find the value of x and y if: 2130x + y012 = 5618
Evaluate: a + ibc + id-c + ida - ib
a + ibc + id-c + ida - ib = (a + ib) (a - ib) - (c + id) (-c + id) = ( a2 - i2b2) - (-c2 + i2d2) = ( a2 + b2) - (-c2 - d2) .........(∵ i2 = -1) = a2 + b2 +c2 + d2)
Find the co-factor of a12 in the following:
2-3560415-7
Evaluate: ∫x21 + x3dx
Evaluate: ∫04dx1 + x2 dx
Find a unit vector in the direction of a →= 3i ^ - 2j^ + 6k
Find the angle between the vectors a→ = i^ - j^ + k^ and b→ = 1^ + j^ - k^
For what value of λ are the vectors a→ = 2i^ + λ j^ + k^ and b→ = i^ - 2j^ -3k^ are perpendicular to each other?