# Topic: Vector Algebra (Test 1)

Topic: Vector Algebra
Q.1
If  are  two collinear vectors, then which of the following are incorrect
A. both the vectors  have same direction, but different magnitudes.
B. the respective components of  are not proportional
C.
D.
Explaination / Solution:

If  are two collinear vectors, then, they are parallel to the same line irrespective of their magnitudes and directions.

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Q.2
Magnitude of the vector   is
A. √63
B. √61
C. √62
D. √65
Explaination / Solution:

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Q.3
Magnitude of the vector  is
A. √3
B. 1
C. 0.5
D. 1.5
Explaination / Solution:

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Q.4
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).
A.
B.
C. -7 and 6; -
D.
Explaination / Solution:

The scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7) is given by : (- 5 – 2 ) i.e. – 7 and (7 – 1 ) i.e. 6. Therefore, the scalar components are – 7 and 6 .,and vector components are -

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Q.5

Find the values of x and y so that the vectors  are equal

A. x = 3, y = 2
B. x = 3, y = 2
C. x = 2, y = 3
D. x = 3, y = 3
Explaination / Solution:

x = 2, y = 3

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Q.6
Find the sum of the vectors
A. i^4j^k^
B. i^+4j^k^
C. i4j^k^
D. i^4j^k^
Explaination / Solution:

We have:
vectors

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Q.7
Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.
A. 32i^12j^
B. 32i^12j^
C. 32i^+12j^
D. 32i^+12j^
Explaination / Solution:

Let be a unit vector in XY plane,making angle 300 with positive X axis,so we have the vector as

is the required vector.

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Q.8
Find the value of x for which is a unit vector
A. ±12
B. ±17
C. ±15
D. ±13
Explaination / Solution:

As x is a unit vector ,
therefore,

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Q.9
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
A.
B.
C.
D.
Explaination / Solution:

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Q.10

A. 13(160i^5j^+70k^)
B. 13(160i^5j^+70k^)
C. 13(160i^5j^-70k^)
D. 13(160i^+5j^70k^)