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Standard XII

Mathematics

Addition of Vectors

Let a,b,c,d...

Question

Let $a, b, c, d$ be the position vectors of the points $A, B, C, D$ respectively. The condition for the figure $A B C D$ to be a parallelogram is

^a +^b =^c +^d

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^a +^b =^c +^d = 0

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^a +^c =^b +^d

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^a +^c =^b +^d = 0

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Solution

The correct option is B $^a +^c =^b +^d$
For $A B C D$ to be a Parallelogram $\to A B | | \to D C$ and $\to A B = \to D C$
So $\to b - \to a = \to c - \to d$
$\to b + \to d = \to a + \to c$ --- (1)
or $\to A D = \to B C$
$\to d - \to a = \to c - \to b$
$\to d + \to b = \to c + \to a$ --- (2)

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Let a,b,c,d be the position vectors of the points A,B,C,D respectively. The condition for the figure ABCD to be a parallelogram is

The correct option is B ^a+^c=^b+^dFor ABCD to be a Parallelogram →AB||→DC and →AB=→DCSo →b−→a=→c−→d→b+→d=→a+→c --- (1)or →AD=→BC→d−→a=→c−→b→d+→b=→c+→a --- (2)

Let $a, b, c, d$ be the position vectors of the points $A, B, C, D$ respectively. The condition for the figure $A B C D$ to be a parallelogram is

The correct option is B $^a +^c =^b +^d$
For $A B C D$ to be a Parallelogram $\to A B | | \to D C$ and $\to A B = \to D C$
So $\to b - \to a = \to c - \to d$
$\to b + \to d = \to a + \to c$ --- (1)
or $\to A D = \to B C$
$\to d - \to a = \to c - \to b$
$\to d + \to b = \to c + \to a$ --- (2)