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Math Assignment | Class XII | Ch-10 | Vector Algebra

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.

Important steps that students need to do
  • First of all students should learn and  revise all basic concepts and formulas of vector algebra.
  • Revise Chapter 10 vector algebra  NCERT book of Mathematics.
  • Revise all examples of chapter 10 of  NCERT book.
  • Now start the Assignment.

Assignment on Vector Algebra

Question 1 :
Show that the points with position vector  equation  and  equation 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 : equation

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  equation  and equation  are equal.

Ans: x = y = 2, x = 1

Question 5 :

equation then find a vector of magnitude 6 units which is parallel to the vector  equation

Answer : 

equation 
Question 6 :
Find a vector a of magnitude 5√2  square unit making an angle of  equation  with x-axis, equation  with the y-axis and an acute angle θ with the z-axis
Answer:  equation

Questions based of the scalar or dot product

Question 7 : If two vectors  equation and  equation are such that equation = 3 and equation = 2 and equation =4 then find the value of   equation.      
Answer : 2

Question 8: If the angle between two vectors equation and  equation  of equal magnitude is equation and their dot product is equation then find their magnitudes
Answer:   equation
Question 9: Find the cosine of the acute angle which the vector equation makes with y-axis.
Ans: 1/2
Hint: Find the dot product between the given vector and the unit vector along y-axis.

Question 10: Find λ so that the projection of  equation  on  equation is 4 units
Answer: 5

Question 11:: Find equation if  equation  and    equation = 4
Answer: equation

Question 12 : If equation and  equation  are two unit vectors and equation is also a unit vector then find the angle between equation and  equation.

Answer: equation 

Question 13 : Let  equation  be three vectors of magnitude 3, 4, 5 respectively. If each one is perpendicular to the sum of the other two vectors then prove that: 
equation

Question 14: If equation and  equation and  equation , then find the angle between 
equation  and  equation 
Answer :  equation 
Hint: Bring vector c to the RHS and then squaring on both side
Question 15 : Express the vector  equation  as the sum of two vectors such that one is parallel to the vector  equation  and the other is perpendicular to equation 
Answer:  equation
Hint : Let equation find equation  now find equation by using  equation . Now find the value of λ by using equation

Question 16 Express the vector equation  as the sum of two vectors such that one is parallel to the vector  equation  and the other is perpendicular to  equation 
Answer: equation

Question 17: Dot product of a certain vector with vectors  equation  and equation  are respectively  -1, 6 and 5. Find the vector 
Answer: equation

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  equation,  equation  and  equation  find λ such that equation is perpendicular to equation
Answer λ = 5

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

Question 19: Find the angle between equation  and  equation  if  equation  and  equation 
Answer:  equation 

Question 20
 are unit vectors, suppose  and angle between  and  is  .
Then prove that 

Solution Hint:



Questions based on the Vector or cross  product

Question 21
If  equation  and   equation then find the value of λ so that  equation and  equation are parallel vectors.

Question 22
Let equation,  equation  and  equation then find equation  which is perpendicular to both equation  and  equation  and equation
Answer:  equation

Question 23
Let equation  , equation and  equation  then find  equation  which is perpendicular to both  equation  and equation and equation

Answer: equation

Question 24
Find a vector of magnitude 8 which is perpendicular to both vectors  equation  and equation
Answer:  equation 

Question 25
If  equation and equation then find a unit vector which is perpendicular to both the vectors equation  and  equation 
Answer:   equation 

Question 26
If  equation  , equation  and equation  then calculate  equation 
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:   equation 

Question 28
If  equation and equation then show that equation  is parallel to equation .
Solution Hint: Find equation  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 equation  units that are perpendicular to the plane of vectors  equation  and  equation 
Answer: equation 

Question 30
If  equation  and  equation  are unit vectors then find the angle between  equation  and  equation  if  equation is a unit vector.
Answer:  equation 

Question 31
If  equation  and  equation  , then find equation 
Answer:  4
Hint : Using Lagrange's identity here.

Question 32
If equation  , equation  and  equation are three vectors, find the area of parallelogram having diagonals equation  and equation 
Answer:  equation 

Question 33
Two adjacent sides of a parallelogram are equation  and  equation . Find the unit vector parallel to one of its diagonals. Also find its area 
Answer: 
Required unit vector is  equation  Area = equation  square unit.

Questions based on the scalar triple  product

Note: These questions are deleted from CBSE syllabus
Question 34
Find λ so that the four points with position vectors  equation ,  equationequation and  equation are coplanar 
Answer : λ = 5

Question 35
Find the volume of the parallelopiped whose coterminous edges are equation ,equation  and equation  
Answer: 2

Question 36
The volume of the parallelopiped whose coterminous edges are equation ,  equation  and  equation  is 546 cubic unit. Find λ
Answer : λ = -3

Question 37
(i)  equation 

(ii)  equation 

(iii)  equation 

Question 38
If the vectors equationequation  and  equation are coplanar then find the value of equation.
Answer: -2

Question 39
Let equation,  equation  and  equation is a vector such that equation  and equation  then find the value of equation 
Answer: 19/2

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

Question 40
If  equation  , equation and equation  be coplanar vectors, then find the value of equation  
Answer: equation

Question 41
Let equation and equation  be two vectors a vector perpendicular to both the vectors equation and equation has the magnitude 12 then find the vector.
Answer: equation

Solution Hint: Required vector is equation and equation.
Find λ and then the required vector


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