Let A- - - - - and- B- - 2- - - The magnitude of a coplanar vector C- such that A-C- - B-C- - A-B- is given by

The correct option is D √(59) Let the vector C⃗ be x î+ y ĵ A⃗·B⃗= (î + ĵ)· #160; (2î ĵ)=1 Given: A⃗·C⃗ = B⃗·C⃗ = A⃗·B⃗=1 , A ...

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Byju's Answer

Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

Let A⃗ = î ...

Question

Let $\to A = (^i +^j)$ and, $\to B = (2^i -^j)$ . The magnitude of a coplanar vector $\to C$ such that $\to A \cdot \to C = \to B \cdot \to C = \to A \cdot \to B$ , is given by

\sqrt{\frac{5}{9}}

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\sqrt{\frac{10}{9}}

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\sqrt{\frac{20}{9}}

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\sqrt{\frac{9}{12}}

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Solution

The correct option is D $\sqrt{\frac{5}{9}}$
Let the vector $\to C$ be $x^i + y^j$
$\to A \cdot \to B = (^i +^j) \cdot (2^i -^j) = 1$

Given: $\to A \cdot \to C = \to B \cdot \to C = \to A \cdot \to B = 1$ ,

$\to A . \to C = x + y = 1$ ......(1)

and $\to B . \to C = 2 x - y = 1$ ........(2)

Solving these two equations simultaneously

$x = 2 / 3$ and $y = 1 / 3$

Hence $| \to C | = \sqrt{\frac{4}{9} + \frac{1}{9}} = \sqrt{\frac{5}{9}}$

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Similar questions

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Let →A=(^i+^j) and, →B=(2^i−^j). The magnitude of a coplanar vector →C such that →A⋅→C=→B⋅→C=→A⋅→B, is given by

The correct option is D √59Let the vector →C be x^i+y^j→A⋅→B=(^i+^j)⋅(2^i−^j)=1Given: →A⋅→C=→B⋅→C=→A⋅→B=1,→A.→C=x+y=1 ......(1)and →B.→C=2x−y=1 ........(2)Solving these two equations simultaneouslyx=2/3and y=1/3Hence |→C|=√49+19=√59

Let $\to A = (^i +^j)$ and, $\to B = (2^i -^j)$ . The magnitude of a coplanar vector $\to C$ such that $\to A \cdot \to C = \to B \cdot \to C = \to A \cdot \to B$ , is given by