Show that ( a - b) ( a + b) = 2( a b)

( a - b) ( a + b) = a a + a b - b a - b b = a b + a b = 2( a b) [ and b a = - a b ]

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 454,Ex.10.4,Q.No 4

Question

Show that $(\vec a - \vec b) \times (\vec a + \vec b) = 2(\vec a \times \vec b)$

Step-by-step Solution

$(\vec a - \vec b) \times (\vec a + \vec b)$
$= \vec a \times \vec a + \vec a \times \vec b - \vec b \times \vec a - \vec b \times \vec b = \vec a \times \vec b + \vec a \times \vec b = 2(\vec a \times \vec b)$

[ and $\vec b \times \vec a = - \vec a \times \vec b$]

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