SATHEE: Vectors 2 Question 14

Vectors 2 Question 14

14. Let the vectors $\vec{P Q}, \vec{Q R}, \vec{R S}, \vec{S T}, \vec{T U}$ and $\vec{U P}$ represent the sides of a regular hexagon.

Statement I $\vec{P Q} \times (\vec{R S} + \vec{S T}) \neq \vec{0}$ .

because

Statement II $\vec{P Q} \times \vec{R S} = \vec{0}$ and $\vec{P Q} \times \vec{S T} \neq \vec{0}$

(2007, 3M)

Show Answer

Answer:

Correct Answer: 14. (c)

Solution:

Since, $\vec{P Q}$ is not parallel to $\vec{T R}$ .

$∵ \vec{T R}$ is resultant of $\vec{R S}$ and $\vec{S T}$ vectors. $\Rightarrow \vec{P Q} \times (\vec{R S} + \vec{S T}) \neq \vec{0}$ .

But for Statement II, we have

$\vec{P Q} \times \vec{R S} = \vec{0}$

which is not possible as $\vec{P Q}$ not parallel to $\vec{R S}$ .

Hence, Statement I is true and Statement II is false.

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Vectors 2 Question 14

14. Let the vectors PQ→,QR→,RS→,ST→,TU→ and UP→ represent the sides of a regular hexagon.

Answer:

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14. Let the vectors $\vec{P Q}, \vec{Q R}, \vec{R S}, \vec{S T}, \vec{T U}$ and $\vec{U P}$ represent the sides of a regular hexagon.