**Maths Assignment Class 12**

**Vector Algebra Chapter 10**

*Extra questions important for the examination. Maths assignment on vector algebra for complete knowledge of the concept.*

**Assignment on Vector Algebra**

**Question 1 :**

**Show that the points with position vector **, and are collinear vectors.

**Hint: Let given vectors are the position vectors of point A, B and C.****Find vector AB and AC. If one vector is the scalar multiple of the other then they are called parallel vectors. **

**Also these are co-initial vectors so these vector are called collinear vectors.**

**Question 2 : If A is a point (1, -2) and the vector AB has component 2 and 3, find the coordinates of point B.****Ans: (3, 1)**

**Hint : **

**Question 3 :** **Using vectors prove that the points A(-1, 2), B(0, 0), C(2, -4) are collinear.**

**Question 4 : ****Find the values of x, y, z so that the vector ** and are equal.Ans: x = y = 2, x = 1

**Question 5 :**If then find a vector of magnitude 6 units which is parallel to the vector

Answer : **Question 6 :**

Find a vector a of magnitude 5√2 square unit making an angle of Ï€/4 with x - axis, Ï€/2 with the y - axis and an acute angle Î¸ with the z - axis

Answer:

**Answer: ****Hint : Let find now find by using . Now find the value of Î» by using ****Question 16 Express the vector **** as the sum of two vectors such that one is parallel to the vector **** and the other is perpendicular to ****Answer: ****Question 17: Dot product of a certain vector with vectors **, **and **** are respectively -1, 6 and 5. Find the vector. ****Answer: ****Hint : Consider a required vector in general form with components x, y, z, then find its dot product with all the given vectors and then solve the different equations.**

**Question 18: If ****, **** and **** find Î» such that **** is perpendicular to **

**Answer Î» = 5**

**Hint : Two vectors are perpendicular if their dot product is zero**

**Question 19: Find the angle between **** and **** if ** **and ****Answer: 0**

**Question 20**

** are unit vectors, suppose **** and angle between **** and **** is **Ï€/6**. ****Then prove that ****Solution Hint:**

⇒ Î» = åœŸ 2

**Answer: ****Î» = **åœŸ 1

**Question 22**

**Let ****, **** and **** then find **** which is perpendicular to both **** and **** and ****Answer: ****Question 23**

**Let **** , **** and **** then find **** which is perpendicular to both **** and **** and **

**Answer: ****Question 24**

**Find a vector of magnitude 8 which is perpendicular to both vectors **** and **.**Answer: **** **

**Question 25**

**If **** and **** then find a unit vector which is perpendicular to both the vectors **** and **** ****Answer: **** ****Question 26**

**Answer: 45**

**Question 27**

**Using vectors find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5), C(1, 5, 5)**

**Answer: **** ****Question 28**

**If **** and **** then show that **** is parallel to **** ****Solution Hint: **

**Find **** then using the given conditions, if this product is = 0 then the vectors are perpendicular to each other.**

**Question 29**

**Find the vectors of magnitude **** units that are perpendicular to the plane of vectors **** and **** ****Answer: **** **

**Question 30**

**If and are unit vectors then find the angle between and if is a unit vector.****Answer: **Ï€/6

**Question 31**

**Answer: 4**

**Hint : Using Lagrange's identity here.**

**Question 32**

**If **** , **** and **** are three vectors, find the area of parallelogram having diagonals **** and ****Answer: **** **

**Question 33**

**Two adjacent sides of a parallelogram are **** and **** . Find the unit vector parallel to one of its diagonals. Also find its area ****Answer: **

**Required unit vector is **** Area = **** square unit.**

**Questions based on the scalar triple product**

**Note: These questions are deleted from CBSE syllabus**

**Question 34**

**Find Î» so that the four points with position vectors , , and are coplanar ****Answer : Î» = 5**

**Question 35**

**Find the volume of the parallelopiped whose coterminous edges are , and ****Answer: 2**

**Question 36**

**The volume of the parallelopiped whose coterminous edges are , and is 546 cubic unit. Find Î»****Answer : Î» = -3**

**Question 37**

**(i) **

**(ii) **

**(iii) **

**Question 38**

**If the vectors , and are coplanar then find the value of .****Answer: -2**

**Question 39**

**Let , and is a vector such that and then find the value of ****Answer: 19/2**

**Solution Hint**

**Let now using and and by compairing the components find the relations between a, y, z. Solve these relations for the value of x, y, z, then find and its magnitude.**

**Question 40**

**If , and be coplanar vectors, then find the value of ****Answer: **

**Question 41**

**Let and be two vectors a vector perpendicular to both the vectors and has the magnitude 12 then find the vector.****Answer: **

**Solution Hint: Required vector is and .****Find Î» and then the required vector**

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