EXERCISE 6.2

EXERCISE 6.2 1. If 3 , 2 , k b k c , find  . 2. Find the volume of the parallelepiped whose coterminous edges are represented by the vectors 14 10 , 14 3. The volume of the parallelepiped whose coterminus edges are 3 , k i is 90 cubic units. Find the value of λ . 4. If , , a b c  are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of ( ) ( ) ( ) ( 5. Find the altitude of a parallelepiped determined by the vectors ˆ ˆ 3 , k b = + if the base is taken as the parallelogram determined by b and c  . 6. Determine whether the three vectors k i are coplanar. 7. Let k b = + 3 ˆ c i c j c k . If c = and c = , find 3 c such that , a b c  are coplanar. 12th_Maths_EM_Vol1_CH 6 Vector Algebra.indd 237 12th_Maths_EM_Vol1_CH 6 Vector Algebra.indd 237 21/11/2024 17:30:06 21/11/2024 17:30:06 238 8. If (1 ) , (1 ) , k b xi x k c yi xj y k show that [ , , ] a b c  depends on neither x nor y . 9. If the vectors ai aj ck i ci cj bk are coplanar, prove that c is the geometric mean of a and b . 10. Let , , a b c  be three non-zero vectors such that c  is a unit vector perpendicular to both a  and b If the angle between a  and b is 6 π , show that [ , , ] | | a b c