The vector hati+x hatj+3 hatk is rotated through an angle θ and doubled in magnitude, then it becomes 4 hati+(4x-2) hatj+2 hatk . The value of x is

Question

The vector hati+x hatj+3 hatk is rotated through an angle θ and doubled in magnitude, then it becomes 4 hati+(4x-2) hatj+2 hatk . The value of x is (A)  -(2/3), 2  (B)  (1/3), 2  (C)  (2/3), 0  (D)  2, 7

Tardigrade Admin · Accepted Answer

We have, 2| hati+x hatj+3 hatk| =|4 hati+(4x-2) hatj+2 hatk| ⇒ 2√1+x2+9=√42+(4x-2)2+22 ⇒ 4(x2+10)=16+16x2+4-16x+4 ⇒ 12x2-16x-16=0 ⇒ 3x2-4x-4=0 ⇒ (3x+2)(x-2)=0 ⇒ x=2, -(2/3)

Q. The vector $\hat{i} + x \hat{j} + 3 \hat{k}$ is rotated through an angle $θ$ and doubled in magnitude, then it becomes $4 \hat{i} + (4 x - 2) \hat{j} + 2 \hat{k}$ . The value of $x$ is

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

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

${\frac{2}{3}, 0}$

${2, 7}$

Q. The vector i^+xj^​+3k^ is rotated through an angle θ and doubled in magnitude, then it becomes 4i^+(4x−2)j^​+2k^ . The value of x is

{−32​,2}

{31​,2}

{32​,0}

{2,7}

We have, 2∣∣​i^+xj^​+3k^∣∣​ =∣∣​4i^+(4x−2)j^​+2k^∣∣​ ⇒21+x2+9​=42+(4x−2)2+22​ ⇒4(x2+10)=16+16x2+4−16x+4 ⇒12x2−16x−16=0 ⇒3x2−4x−4=0 ⇒(3x+2)(x−2)=0 ⇒x=2, −32​

Q. The vector $\hat{i} + x \hat{j} + 3 \hat{k}$ is rotated through an angle $θ$ and doubled in magnitude, then it becomes $4 \hat{i} + (4 x - 2) \hat{j} + 2 \hat{k}$ . The value of $x$ is

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

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

${\frac{2}{3}, 0}$

${2, 7}$