The equation of the plane passing through three non-collinear points a→, b→, c→ is :
r→ . b→ × c→ + c→ × a→ + a→ × b→ = 0
r→ . b→ × c→ + c→ × a→ + a→ × b→ = a→ b→ c→
r→ . a→ × b→ × c→ = a→ b→ c→
r→ . a→ + b→ + c→ = a→ b→ c→
The unit vector perpendicular to i^ - j^ and coplanar with i^ + 2j^ and 2i^ + 3j^ is :
2i^ - 5j^29
2i^ + 5j^
i^ + j^2
i^ + j^
a→ × b→2 + a→ . b→2 is equal to :
a→2 b→2
a→2 + b→2
1
2a→ . b→
∫32 x3 logx2dx is equal to
8x4(log(x))2 + c
x48logx2 - 4logx + 1 + c
8logx2 - 4logx + c
x38logx2 - 2logx + c
∫cosx - 1sinx + 1exdx is equal to :
excosx1 + sinx + c
c - exsinx1 + sinx
c - ex1 + sinx
c - excosx1 + sinx
If ∫fxdx = gx + c, then ∫f-1xdx is equal to :
xf-1(x) + c
f(g-1(x)) + c
xf-1(x) - g(f-1(x)) + c
g-1(x) + c
The value of ∫12dxx1 + x4 is :
14log1732
14log3217
log172
14log172
The value of the integral ∫abxdxx + a + b - x is :
π
12b - a
π/2
b - a
B.
Let I = ∫abxdxx + a + b - x ...i∴ I = ∫aba + b - xa + b - x + x ...iiOn adding Eqs. (i) and (ii), we get 2I = ∫abdx = xab = b - a∴ I = 12b - a
The area bounded by y = log(x), x-axis and ordinates x = 1, x = 2 is
12log22
log(2/e)
log(4/e)
log(4)
The area of the segment of a circle of radius a subtending an angle of 2α at the centre is :
a2α + 12sin2α
12a2sin2α
a2α - 12sin2α
a2α