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Problem Questions with Answer, Solution - Exercise 6.2: Scalar triple product | 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Chapter: 12th Mathematics : UNIT 6 : Applications of Vector Algebra

Exercise 6.2: Scalar triple product

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EXERCISE 6.2

 

1. 


2. Find the volume of the parallelepiped whose coterminous edges are represented by the vectors -6iˆ +14ˆ+10kˆ14iˆ - 10ˆ6kˆ and 2iˆ ˆ- 2kˆ .


3. The volume of the parallelepiped whose coterminus edges are 7iˆ + λ ˆ 3kˆiˆ + 2 ˆ kˆ3iˆ + 7 ˆ+ 5kˆ is 90 cubic units. Find the value of λ .


4. If , 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  = 2+ 5 + 3k = + 3  2k  and   = -3+  2 if the base is taken as the parallelogram determined by and .


6. Determine whether the three vectors 2iˆ + 3 ˆ+ kˆiˆ  2 ˆ+ 2kˆ and 3iˆ + ˆ+ 3kˆ are coplanar.


7. Let  = ˆ+ ˆ+ ˆk = and = c1ˆ+ cˆ+ c3ˆ. If c= 1 and c= 2 , find csuch that , and  are coplanar.


8. If  show that [] depends on neither x nor y .


9. If the vectors are aiˆ ˆ+ akˆ , iˆ kˆ  and ciˆ ˆ+ bkˆ  are coplanar, prove that is the geometric  mean of and .


10. Let , be three non-zero vectors such that  is a unit vector perpendicular to both and  . If the angle between  and  is π/6. Show that 



Answers:

1. 24

2. 720 cubic units

3. −5

4. ±12

5. 2√3 / 5

6. coplanar

7. 2


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12th Mathematics : UNIT 6 : Applications of Vector Algebra : Exercise 6.2: Scalar triple product | Problem Questions with Answer, Solution

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12th Mathematics : UNIT 6 : Applications of Vector Algebra


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