Test: Scalar Product Of Two Vectors


5 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Scalar Product Of Two Vectors


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QUESTION: 1

If   are any two vectors, then

Solution:

|a+b| ≤ |a| + |b|
Let us take an example : a = 1, b= 2
|1 + 2| ≤ |1| + |2|
|3| ≤ |3|
Hence, proved

QUESTION: 2

The angle between the vectors is:    is :

Solution:

a = 6i - 3j + 2k      b = 2i + j - 2k
a.b = 12 - 3 - 4 = 5
|a| = [(6)2 + (-3)2 + (2)2]1/2 
|a| = [36 + 9 + 4]½
|a| = (49)½
|a| = 7
|b| = [(2)2 + (1)2 + (-2)2]½
|b| = [4 + 1 + 4]½
|b| = 3
Cosθ = (a.b)/|a||b|
= 5/(7)(3)
= 5/21
θ = cos-1(5/21)

QUESTION: 3

If  are two vectors, such that , then = ……​

Solution:

 |a - b|2 = |a|2 + |b|2 - 2|a||b|
|a - b|2  = (3)2 + (2)2 - 2(5)
|a - b|2  = 9 + 4 - 10
|a - b|2  = 3 
|a - b|   = (3)½.

QUESTION: 4

The projection of the vector  on the vector is:​

Solution:

Projection = (A.B)/|B|
= [(i + 2j + k) . (2i + 3j + 2k)]/[(2)2 + (3)2 + (2)2]½
= (2 + 6 + 2)/[4 + 9 + 4]½
= 10/(17)1/2

QUESTION: 5

The angle between two non-zero vectors  is given by

Solution:

A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers. We usually use the symbol an to represent a sequence, where n is a natural number and an is the value of the function on n. A sequence may be finite or infinite.

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