Question

the nitrogen does not form NF₃ because 1. the bond energy of NΞΝ is very high 2. vacant d-orbital is not present 3. N belongs to 4 group 4. there is inert effect Q. in which of the following compound there are max. no. of sp² hybrid C atoms 1. benzene 2. 1,2,4-hexatriene 3. 1,3,5-hexatriene 4. both 1 and 2

Answer 1

Answer:

Three points are said to be collinear if they all lie in a straight line.

If Three points (x1, y1), (x2, y2), (x3, y3) are collinear then no triangle can be formed using three points and so the area formed by the triangle by the three points is zero.

Area of Triangle = 1/2 [x1 (y2 − y3) + x2 (y3 − y1) + x3 (y1 − y2)]                           ...(1)

1. For triangle, A(-1, -1), B(0, 1), C(1, 3)

Area =  

      = 1/2 [ -1(-2) + 0(3+1) + 1(-1-1)]            = 1/2 [2 + 0 - 2]       = 1/2 [2-2]     = 0Hence the points are collinear

2. For triangle, D(-2, -3), E(1, 0), F(2, 1)

Using 1,

Area = 1/2 [-2(0-1) + 1(1-(-3)) + 2(-3-0)]       = 1/2 [-2(-1) + 1(1+3) + 2(-3)]      = 1/2 [ 2 + 4 -6 ]     = 1/2 [ 6 - 6 ]     = 1/2 (0)    = 0Hence the points are collinear.

3. For triangle, L(2, 5), M(3, 3), N(5, 1)

Using 1,

Area = 1/2 [2(3-1) + 3(1-5) + 5(5-3)]       = 1/2 [ 2(2) + 3(-4) + 5(2)]      = 1/2 [ 4 - 12 + 10 ]     = 1/2 [ 14 - 12 ]         = 1/2 (2)    = 1

Hence the points are not collinear.

4. For triangle, P(2, -5), Q(1, -3), R(-2, 3)

Using 1,Area = = 0

Area = 1/2 [ 2(-3-3) + 1(3-(-5)) + (-2)(-5-(-3))]       = 1/2 [ 2(-6) + 1(3+5) - 2 (-5+3)]      = 1/2 [ -12 + 8 -2(-2)]     = 1/2 [-12 + 8 +4]    = 1/2 [ -12 + 12]   = 1/2 (0)

  = 0

Hence the points are collinear.

5. For triangle, R(1, -4), S(-2, 2), T(-3, 4)

Area =

Hence the points are collinear.

6. For triangle, A(-4, 4), K(-2, 5/ 2 ), N(4, -2)

Area =

Hence the points are collinear.

Explanation: