Given that a b = 0 and a b = 0 . What can you conclude about the vectors a and b?

a b = 0 and a b = 0 ( a = 0 ;or ; b = 0 ;or ; a b) and ( a = 0 or b = 0 or a|| b ) Either a = 0 or b = 0 [ and are not valid at the same time]

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 454,Ex.10.4,Q.No 6

Question

Given that $\vec a \cdot \vec b = 0$ and $\vec a \times \vec b = \vec 0$. What can you conclude about the vectors $\vec a$ and $\vec b?$

Step-by-step Solution

$\vec a \cdot \vec b = \vec 0$ and $\vec a \times \vec b = \vec 0$

$\Rightarrow (\vec a = \vec 0\;or\;\vec b = \vec 0\;or\;\vec a \bot \vec b)$ and $(\vec a = \vec 0$ or $\vec b = \vec 0$ or $\vec a||\vec b$)

$\Rightarrow$ Either $\vec a = \vec 0$ or $\vec b = \vec 0$

[ and are not valid at the same time]

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.