Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# If → a × → B = 0 Can You Say that (A) → a = → B , (B) → a ≠ → B - Physics

If $\vec{A} \times \vec{B} = 0$ can you say that

(a) $\vec{A} = \vec{B} ,$

(b) $\vec{A} \neq \vec{B}$ ?

#### Solution

If  $\vec{A} \times \vec{B} = 0$, then both the vectors are either parallel or antiparallel, i.e., the angle between the vectors is either $0^\circ \text { or } 180^\circ$.

$\vec{A} \vec{ B } \sin\ \theta \ \hat { n } = 0.......\left(\because \sin0^\circ= \sin180^\circ = 0\right)$

Both the conditions can be satisfied:

(a) $\vec{A} = \vec{B} ,$ i.e., the two vectors are equal in magnitude and parallel to each other

(b) $\vec{A} ≠ \vec{B} ,$  i.e., the two vectors are unequal in magnitude and parallel or anti parallel to each other.

Concept: What is Physics?
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Chapter 2: Physics and Mathematics - Short Answers [Page 28]

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Short Answers | Q 13 | Page 28
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