NDA 2023 Maths · Mathematics · Vector Algebra · hard

The sides of a triangle, taken in order, are represented by vectors vec a,vec b,vec c of lengths 3, 5 and 7 units so that their sum is the zero…

Single correct option

The sides of a triangle, taken in order, are represented by vectors

\vec a,\vec b,\vec c

of lengths

3

5

and

7

units so that their sum is the zero vector. When

\vec a

and

\vec b

are drawn from a common initial point, the angle between them is

Show answer and solution

Answer: (C) $60^\circ$

From

\vec c=-(\vec a+\vec b)

|\vec c|^2=|\vec a|^2+|\vec b|^2+2\vec a\cdot\vec b

, i.e.

49=9+25+30\cos\theta

. So

\cos\theta=\dfrac{15}{30}=\dfrac12

and

\theta=60^\circ

. The angle

120^\circ

is the angle in the triangle formed by the sides, which is the supplement.

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