The vector -x-3k- is rotated through an angle - and is doubled in magnitude- It now becomes 4-4x-2- -2k- The possible values of x isare

Since, the vector î+xĵ+3k̂ is doubled in magnitude then it becomes, 4î+(4x−2)ĵ +2k̂ 2|î+xĵ+3k̂| = |4î+(4x−2)ĵ +2k̂| ⇒ 2√(1+x^2+9) = √(16 + (4x 2)^2 + 4) ⇒40 ...

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Standard XII

Mathematics

Domain

The vector î+...

Question

The vector $^i + x^j + 3^k$ is rotated through an angle $θ$ and is doubled in magnitude. It now becomes $4^i + (4 x - 2)^j + 2^k$ . The possible value(s) of $x$ is(are)

{2, - \frac{2}{3}}

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{\frac{1}{3}, 2}

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\frac{2}{3}

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- \frac{1}{3}

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Solution

The correct option is A ${2, - \frac{2}{3}}$
Since, the vector $^i + x^j + 3^k$ is doubled in magnitude then it becomes, $4^i + (4 x - 2)^j + 2^k$
$2 |^i + x^j + 3^k | = | 4^i + (4 x - 2)^j + 2^k |$
$\Rightarrow 2 \sqrt{1 + x^{2} + 9} = \sqrt{16 + (4 x - 2)^{2} + 4}$
$\Rightarrow 40 + 4 x^{2} = 20 + (4 x - 2)^{2}$
$\Rightarrow 3 x^{2} - 4 x - 4 = 0$
$\Rightarrow (x - 2) (3 x + 2) = 0$
$\Rightarrow x = 2, - \frac{2}{3}$

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Standard XII Mathematics

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The vector ^i+x^j+3^k is rotated through an angle θ and is doubled in magnitude. It now becomes 4^i+(4x−2)^j+2^k. The possible value(s) of x is(are)

The correct option is A {2,−23 }Since, the vector ^i+x^j+3^k is doubled in magnitude then it becomes, 4^i+(4x−2)^j+2^k 2|^i+x^j+3^k|=|4^i+(4x−2)^j+2^k| ⇒2√1+x2+9=√16+(4x−2)2+4 ⇒40+4x2=20+(4x−2)2 ⇒3x2−4x−4=0 ⇒(x−2)(3x+2)=0 ⇒x=2,−23

The vector $^i + x^j + 3^k$ is rotated through an angle $θ$ and is doubled in magnitude. It now becomes $4^i + (4 x - 2)^j + 2^k$ . The possible value(s) of $x$ is(are)