(A) Given $|u+v|^2 = 2(|u|^2+|v|^2)$.Expanding the left side using the property $|a+b|^2 = |a|^2 + |b|^2 + 2(u \cdot v)$:$|u|^2 + |v|^2 + 2(u \cdot v)

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(A) Given $|u+v|^2 = 2(|u|^2+|v|^2)$.Expanding the left side using the property $|a+b|^2 = |a|^2 + |b|^2 + 2(u \cdot v)$:$|u|^2 + |v|^2 + 2(u \cdot v) = 2|u|^2 + 2|v|^2$Rearranging the terms to one side:$|u|^2 + |v|^2 - 2(u \cdot v) = 0$This expression is equivalent to the square of the difference of the vectors:$|u - v|^2 = 0$Taking the square root on both sides:$|u - v| = 0$Therefore,$u - v = 0$,which implies $u = v$.Hence,option $A$ is correct.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

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Let $u$ and $v$ be two vectors in $R^2$. If $|u+v|^2=2(|u|^2+|v|^2)$,then .....

AP EAMCET 2020 All AP EAMCET

A
$u=v$
B
$u$ and $v$ need not be same but they have same direction
C
$u$ and $v$ need not be same but they have the opposite direction
D
$u=2v$

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Basic , Modulus and Algebra of vectors

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Let $u$ and $v$ be two vectors in $R^2$. If $|u+v|^2=2(|u|^2+|v|^2)$,then .....

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Let $b = 3j + 4k$,$a = i + j$ and let $b_1$ and $b_2$ be component vectors of $b$ parallel and perpendicular to $a$ respectively. If $b_1 = \frac{3}{2}i + \frac{3}{2}j$,then $b_2 = $

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