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NCERT Class 12- Mathematics: Chapter β 10 Vector Algebra Part 3
Long Answer (L. A)
Question 8:
Using vectors, prove that .
Answer:
Let be unit vectors making angles A and B, respectively, with positive direction of x-axis. Then
We know
By definition
In terms of components, we have
From (1) and (2) , we get
.
Question 9:
Prove that in a , where a, b, c represent the magnitudes of the sides opposite to vertices A, B, C, respectively.
Answer:
Let the three sides of the triangle BC, CA and AB be represented by and respectively [Fig. 10.2] .
We have
Which pre cross multiplying by , and post cross multiplying by , gives
and
respectively. Therefore,
Dividing by , we get
Objective Type Questions
Choose the Correct Answer from the Given Four Options in Each of the Examples 10 to 21
Question 10:
The magnitude of the vector is
(A)
(B)
(C)
(D)
Answer:
(B) Is the correct answer.
Question 11:
The position vector of the point which divides the join of points with position vectors and in the ratio is
(A)
(B)
(C)
(D)
Answer:
(D) Is the correct answer.
Applying section formula the position vector of the required point is
Question 12:
The vector with initial point and terminal point is
(A)
(B)
(C)
(D) None of these
Answer:
(A) is the correct answer.