Standard XI Physics Chapter 2 - Mathematical Methods Exercise
Mathematical Methods
1. Choose the correct option.
i) The resultant of two forces 10N and 15N acting along the + x and -x axis respectively, is
A) 25 N along + x-axis
B) 25 N along - x-axis
C) 5 N along + x-axis
D) 5 N along - x-axis
Answer : D) 5 N along - x-axis
ii) For two vectors to be equal, they should have the
A) same magnitude
B) same direction
C) same magnitude and direction
D) same magnitude but opposite direction
Answer : C) same magnitude and direction
iii) The magnitude of scalar product of two unit vectors perpendicular to each other is
A) zero
B) 1
C) -1
D) 2
Answer : A) zero
iv) The magnitude of vector product of two unit vectors making an angle 60 degree with each other is
A) 1
B) 2
C) 3/2
D) root3/2
Answer : D) root3/2
v) If A, B and C are three vectors, then which of the following is not correct ?
A) A. (B + C ) = A. B + A. C
B) A. B = B. A
C) AxB = BxA
D) A x ( B + C ) = A x B + B x C
Answer : C ) AxB = BxA
2. Answer the following questions.
i) Show that a = i - j / root 2 is a unit vector
( question is given in image also)
Answer : coming soon..
ii) If v1 = 3i + 4j + k and v2 = i - j - k, determine the magnitude of v1 + v2.
(question is given in image also )
Answer : coming soon...
iii) For v1 = 2i - 3 j and v2 = -6i + 5j, determine the magnitude and direction of v1+v2.
(question is also given in image below)
Answer : coming soon....
iv) Find a vector which is parallel to v = i - 2j and has a magnitude 10. (question is also given in image below)
Answer : coming soon...
v) Show that vectors a = 2i + 5j - 6k and b = i + 5/2 j - 3k are parallel. ( question is also given in image below)
Answer : coming soon...
3. Solve the following problems
Mathematical Methods
1. Choose the correct option.
i) The resultant of two forces 10N and 15N acting along the + x and -x axis respectively, is
A) 25 N along + x-axis
B) 25 N along - x-axis
C) 5 N along + x-axis
D) 5 N along - x-axis
Answer : D) 5 N along - x-axis
ii) For two vectors to be equal, they should have the
A) same magnitude
B) same direction
C) same magnitude and direction
D) same magnitude but opposite direction
Answer : C) same magnitude and direction
iii) The magnitude of scalar product of two unit vectors perpendicular to each other is
A) zero
B) 1
C) -1
D) 2
Answer : A) zero
iv) The magnitude of vector product of two unit vectors making an angle 60 degree with each other is
A) 1
B) 2
C) 3/2
D) root3/2
Answer : D) root3/2
v) If A, B and C are three vectors, then which of the following is not correct ?
A) A. (B + C ) = A. B + A. C
B) A. B = B. A
C) AxB = BxA
D) A x ( B + C ) = A x B + B x C
Answer : C ) AxB = BxA
2. Answer the following questions.
i) Show that a = i - j / root 2 is a unit vector
( question is given in image also)
Answer : coming soon..
ii) If v1 = 3i + 4j + k and v2 = i - j - k, determine the magnitude of v1 + v2.
(question is given in image also )
Answer : coming soon...
iii) For v1 = 2i - 3 j and v2 = -6i + 5j, determine the magnitude and direction of v1+v2.
(question is also given in image below)
Answer : coming soon....
iv) Find a vector which is parallel to v = i - 2j and has a magnitude 10. (question is also given in image below)
Answer : coming soon...
v) Show that vectors a = 2i + 5j - 6k and b = i + 5/2 j - 3k are parallel. ( question is also given in image below)
Answer : coming soon...
3. Solve the following problems