Ncert Exercises & Solutions

Given below in Column-I are the relations between vectors \(a,\) \(b,\) and \(c\) and in Column-II are the orientations of \(a,\) \(b,\) and \(c\) in the \(xy\)-plane. Match the relation in Column-I to the correct orientations in Column-II.

	Column-I		Column-II
(a)	\(a + b = c\)	(i)
(b)	\(a- c = b\)	(ii)
(c)	\(b - a = c\)	(iii)
(d)	\(a + b + c = 0\)	(iv)

Choose the correct option from the given table.

1.	a-(ii), b-(iv), c-(iii), d-(i)
2.	a-(i), b-(iii), c-(iv), d-(ii)
3.	a-(iv), b-(iii), c-(i), d-(ii)
4.	a-(iii), b-(iv), c-(i), d-(ii)

Hint: \(\vec A + \vec B =\vec C\)

Step: Find the correct matches for the given figure.
Consider the adjacent diagram in which vectors \(A\) and \(B\) are corrected by head and tail.

The triangle law of vector addition is gives us;
\(\Rightarrow A + B = C\)
Now analyse each case one by one.
For (a); \(\Rightarrow a + b = c\)
This is represented by the figure (iv).

For (b); \(\Rightarrow a- c = b \Rightarrow a=c +b\)
which is represented by the figure (iii).

For (c); \(\Rightarrow b - a = c \Rightarrow b=c+a\)
which is represented by the figure (i).

For (d); \(\Rightarrow a + b + c = 0\)
is represented by the figure (ii).
Therefore, a-(iv), b-(iii), c-(i), d-(ii) are the accurate matches.
Hence, option (3) is the correct answer.

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