BASIC MATHEMATICS
(Physics)
DPP - 3
VECTOR
Q.1
⃗ = 1î + 2ĵ + 3k̂ and l = 4î + 5ĵ + 6k̂. Find the value of the scalar α
Consider the two vectors: L
⃗ − αl is perpendicular to L
⃗.
such that the vector L
Q.2
Find components of vector a⃗ = î + ĵ + 3k̂ in directions parallel to and perpendicular to vector
⃗b = î + ĵ.
Q.3
(a) Calculate r = a⃗ − ⃗b + c where a⃗ = 5î + 4ĵ − 6k̂ , ⃗b = −2î + 2ĵ + 3k̂ and c = 4î + 3ĵ + 2k̂
(b) Calculate the angle between r and the z-axis.
(c) Find the angle between a⃗ and ⃗b
Q.4
If the velocity of a particle is (2î + 3ĵ − 4k̂) and its acceleration is (−î + 2ĵ + k̂) and angle
between them is
Q.5
nπ
4
. The value of n is.
Consider three vectors ⃗A = î + ĵ − 2k̂, ⃗B = î − ĵ + k̂ and ⃗C = 2î − 3ĵ + 4k̂. A vector ⃗X of the form
⃗ + βB
⃗ ( α and β are numbers) is perpendicular to ⃗C. The ratio of α and β is
αA
(A) 1: 1
Q.6
(B) 2: 1
(C) −1: 1
(D) 3: 1
A string connected with bob is suspended by the point (O) such that it sweeps out conical surface
in horizontal plane. Here r is the position vector of bob, v
⃗ is its velocity and z is the axis of swept
cone as shown. Select INCORRECT statement :-
Q.7
(A) r. z is always zero
(B) r. v
⃗ is always zero
(C) ⃗Z ⋅ v
⃗ is always constant
(D) r ⋅ z is always non zero constant
x-component of a vector ⃗A is twice of its y-component and √2 times of its z-component. Find out
the angle made by the vector from y-axis.
2
1
(A) cos−1 ( )
(B) cos−1 ( )
√7
Q.8
√7
1
2
(C) cos−1 ( )
(D) cos −1 ( )
√6
√6
Given the vectors ⃗A = 2î + 3ĵ − k̂; ⃗⃗⃗⃗B = 3î − 2ĵ − 2kˆ & ⃗C = pî + pĵ + 2pk̂. Find the angle between
⃗ − ⃗B) & ⃗C
(A
2
√3
(A) θ = cos−1 ( )
(B) θ = cos −1 ( 2 )
√3
√2
(C) θ = cos −1 ( 3 )
Q.9
(D) none of these
Find the component of r in the direction of a⃗: −
(A)
⃗ )a
⃗
(r⃗⋅a
a2
(B)
⃗ )a
⃗
(r⃗⋅a
a
(C)
⃗ )r̂
(r⃗⋅a
r
(D)
⃗ )r̂
(r⃗⋅a
r2
Q.10 Statement 1: Unit vector has a unit though its magnitude is one and
Statement 2: Unit vector is obtained by dividing a vector by its own magnitude.
APNI KAKSHA
1
(Physics)
BASIC MATHEMATICS
(A) Statement-1 is true, statement-2 is true and statement- 2 is correct explanation for
statement-1.
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for
statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement- 2 is true.
Q.11 A vector of magnitude 10 m in the direction 37∘ south of west has its initial point at (5 m, 2 m).
If positive x-axis represents the east and positive y-axis the north, the coordinates of its terminal
point are
(A) (−3m, −4m)
(B) (3 m, 4 m)
(C) (−4 m, 6 m)
(D) (−4m, −6m)
Q.12 A plumber steps down 1 m out of his truck and walks 50 m east and then 25 m south, and then
takes an elevator to the basement of the building 9 m below street level. If the east, the north and
the upward direction are represented by the positive x, y and z − axes, which one of the following
represents displacement (meters) of the plumber?
(A) 50î − 25ĵ − 9k̂
(B) 50î + 25ĵ − 9k̂
(C) 50î − 25ĵ − 10k̂
(D) 50î + 25ĵ − 10k̂
APNI KAKSHA
2
BASIC MATHEMATICS
(Physics)
ANSWER KEY
7/16 2.
î + ĵ, 3k̂
3.
(a) 11î + 5ĵ − 7k̂, (b) cos −1 (
4.
(2)
5.
(D)
(B)
7.
11.
(D)
12.
(A)
−7
1.
6.
), (c) cos −1 (
√195
(B)
8.
APNI KAKSHA
(D)
9.
−20
)
√1309
(C)
10.
(D)
3