Maths Book back answers and solution for Exercise questions - Mathematics : Vector Algebra: Scalar triple product: Exercise Questions with Answer, Solution

**EXERCISE 6.2**

** **

**1. **

**2. Find the volume of the parallelepiped whose coterminous edges are represented by the vectors -6 iË† +14Ë†j +10kË†, 14iË† - 10Ë†j - 6kË† and 2iË† + 4 Ë†j - 2kË† .**

**3. The volume of the parallelepiped whose coterminus edges are 7 iË† + Î» Ë†j âˆ’ 3kË†, iË† + 2 Ë†j âˆ’ kË†, âˆ’3iË† + 7 Ë†j + 5kË† is 90 cubic units. Find the value of Î» .**

**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 = âˆ’2i + 5 j + 3k, = i + 3 j âˆ’ 2k and = -3i + j âˆ’ 2k if the base is taken as the parallelogram determined by and .**

**6. Determine whether the three vectors 2 iË† + 3 Ë†j + kË†, iË† âˆ’ 2 Ë†j + 2kË† and 3iË† + Ë†j + 3kË† are coplanar.**

**7. Let = Ë†i + Ë†j + Ë†k, = i and c = c1Ë†i + c2 Ë†j + c3Ë†k . If c1 = 1 and c2 = 2 , find c3 such that , and are coplanar.**

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

**9. If the vectors are a iË† + a Ë†j + akË† , iË† + kË† and ciË† + c Ë†j + bkË† are coplanar, prove that c is the geometric mean of a and b .**

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

**Answers:**

**1. 24**

**2. 720 cubic units**

**3. âˆ’5**

**4. Â±12**

**5. 2âˆš3 / 5**

**6. coplanar**

**7. 2**

Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 6 : Applications of Vector Algebra

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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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