SATHEE: Vectors 1 Question 14

Vectors 1 Question 14

15. Let $\vec{u}, \vec{v}$ and $\vec{w}$ be vectors such that $\vec{u} + \vec{v} + \vec{w} = \vec{0}$ . If $| \vec{u} | = 3, | \vec{v} | = 4$ and $| \vec{w} | = 5$ , then $\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}$ is

(1995, 2M)

(a) 47

(b) -25

(d) 25

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Answer:

Correct Answer: 15. $(3 : 2)$

Solution:

Since, $\vec{u} + \vec{v} + \vec{w} = \vec{0} \Rightarrow | \vec{u} + \vec{v} + \vec{w} |^{2} = 0$

$\Rightarrow | \vec{u} |^{2} + | \vec{v} |^{2} + | \vec{w} |^{2} + 2 (\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$

$\Rightarrow 9 + 16 + 25 + 2 (\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}) = 0$

$\Rightarrow \vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u} = - 25$

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Vectors 1 Question 14

15. Let u→,v→ and w→ be vectors such that u→+v→+w→=0→. If |u→|=3,|v→|=4 and |w→|=5, then u→⋅v→+v→⋅w→+w→⋅u→ is

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15. Let $\vec{u}, \vec{v}$ and $\vec{w}$ be vectors such that $\vec{u} + \vec{v} + \vec{w} = \vec{0}$ . If $| \vec{u} | = 3, | \vec{v} | = 4$ and $| \vec{w} | = 5$ , then $\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} + \vec{w} \cdot \vec{u}$ is