Question

Study the following.List-I List-ll
a)$\overrightarrow{P}.\overrightarrow{Q}$ I)pseudo vector
b)$\overrightarrow{P}\times \overrightarrow{Q}$ II) undefined
c) $\overrightarrow{P}.(\overrightarrow{Q}.\overrightarrow{R})$ III) A Scalar
d)$\overrightarrow{P}\times (\overrightarrow{Q}\times \overrightarrow{R})$ IV) A vector

The correct match is:

• A. A-IV B-III C-I D-II
• B. A-II B-I C-III D-IV
• C. A-III B-IV C-II D-I
• D. A-I B-II C-IV D-III

Answer 1

Answer: (C)

A-III B-IV C-II D-I

(a) $\overrightarrow{P}\cdot \overrightarrow{Q}=$

A scalar because product comes out as a scalar quantity

(b) $\overrightarrow{P}\times \overrightarrow{Q}=$ A vector because product is a vector

(c) $\overrightarrow{P}\cdot (\overrightarrow{Q}\cdot \overrightarrow{R})=$ undefined because dot product of $\overrightarrow{Q}$ and $\overrightarrow{R}$ is a scalar as it is a dot product and when we do $\overrightarrow{P}\cdot scalar$ then due to dot product it should be a scalar but as it is a product of a vector and scalar so it may be vector so there is nothing definite or we can say undefined.

(d) $\overrightarrow{P}\times (\overrightarrow{Q}\times \overrightarrow{R})=$ A pseudo vector a vector whose direction will get reversed in a reflection pattern whereas any other vector will remain same in the direction when reflected.