Vectors:Class 12th:DPP

Vectors
Q1 Solve the following-                                          
Show that the vectors

4i+13j-18k,

 i-2j+3k,

2i+3j-4k are coplaner                          (3)

Q2 if a,b,c are non co-planer vectors then prove that the vectors a+b+c ,a+b-3c, a+4b-9c are collinear.                                (3)     
Q3 Prove the section formula for internal division  (4)
Q4 If the three points A(3,2,p),B(q,8,-10) and c(-2,-3,1) are collinear then find 
i) the ratio in which point C divides line segment AB
ii) the values of p and q                                              (4)
Q5 Prove that the medians of triangle are concurrent. (3)
Q6 Prove that the angle subtended on a semicircle is a right angle. (3)