revision

integrate 1/(x+2)^(1/2)

please who knows a good furthermaths text book for beginners???

Solution 

(i) Finding and

from the question,

So

Substituting the values of and in the third equation verfifies. 

(ii) Stating the vectors a and b

(iii) Showing that a and b are linearly independent

Therefore a and b are linearly independent.

(iv) Finding the cartesian equation of the plane containing a and b

Normal to the plane

Let P be a general point on the plane with coordinates: 

Using vector a

So the plane has equation

N/B: One could equally use vector b or any other vector on the plane to get the equation. Note also that any vector parallel to vector n is equally a normal to the plane and can be used to get the equation of the plane. 

Given the two vectors

and

 (i) Calculate the values of and (3mks)

(ii) By using the values of and , state the vectors a and b (1mk)

(iii) Show that a and b are linearly independent (2mks)

(iv)Find the cartesian equation of th plane containing a and b. (2mks)

June 2019 question 8 

June 2019 question 8