If the vectors vec a =x hat i +y hat j +z hat k and such that vec a , vec c and vec b form a right handed system, then vec c is :

Question

If the vectors vec a =x hat i +y hat j +z hat k and such that vec a , vec c and vec b form a right handed system, then vec c is : (A) z hat i -x hat k  (B)  vec0 (C) y hat j  (D) -z hat i +x hat k

Tardigrade Admin · Accepted Answer

Given that veca = x hat i + y hatj + z hatk and vecb = hatj are such that veca. vecc and vecb form a right handed system ∴ vecc = vecb × veca = | hati& hatj& hatk 0&1&0 x&y&z| = hati z - x hatk

Q. If the vectors $a = x \hat{i} + y \hat{j} + z \hat{k}$ and such that $a, c$ and $b$ form a right handed system, then $c$ is :

$z \hat{i} - x \hat{k}$

$0$

$y \hat{j}$

$- z \hat{i} + x \hat{k}$

Given that $a = x \hat{i} + y \hat{j} + z \hat{k}$ and $b = \hat{j}$ are
such that $a . c$ and $b$ form a right handed system
$∴ c = b \times a = ∣ ∣ \hat{i} 0 x \hat{j} 1 y \hat{k} 0 z ∣ ∣$
$= \hat{i} z - x \hat{k}$

Q. If the vectors a=xi^+yj^​+zk^ and such that a,c and b form a right handed system, then c is :

zi^−xk^

0

yj^​

−zi^+xk^

Given that a=xi^+yj^​+zk^ and b=j^​ are such that a.c and b form a right handed system ∴c=b×a=∣∣​i^0x​j^​1y​k^0z​∣∣​ =i^z−xk^

Q. If the vectors $a = x \hat{i} + y \hat{j} + z \hat{k}$ and such that $a, c$ and $b$ form a right handed system, then $c$ is :

$z \hat{i} - x \hat{k}$

$0$

$y \hat{j}$

$- z \hat{i} + x \hat{k}$

Given that $a = x \hat{i} + y \hat{j} + z \hat{k}$ and $b = \hat{j}$ are
such that $a . c$ and $b$ form a right handed system
$∴ c = b \times a = ∣ ∣ \hat{i} 0 x \hat{j} 1 y \hat{k} 0 z ∣ ∣$
$= \hat{i} z - x \hat{k}$