hatu and hatv are unit vectors such that hatu . hatv = 0 . If vecr is any vector coplanar with vecu and vecv then the magnitude of the vector vecr × ( hatu × hatv) is :

Question

hatu and hatv are unit vectors such that hatu . hatv = 0 . If vecr is any vector coplanar with vecu and vecv then the magnitude of the vector vecr × ( hatu × hatv) is : (A)  0  (B)  1  (C)  | vecr|  (D)  2| vecr|

Tardigrade Admin · Accepted Answer

Given, | vecu|=| vecv|=1 and vecu . vecv=0 ie, angle between vecu and vecv is 90o ∴ | vecu× vecv| =| vecu|| vecv| sin θ =1

Q. $\overset{u}{^}$ and $\overset{v}{^}$ are unit vectors such that $\overset{u}{^} . \overset{v}{^} = 0$ . If $r$ is any vector coplanar with $u$ and $v$ then the magnitude of the vector $r \times (\overset{u}{^} \times \overset{v}{^})$ is :

$0$

$1$

$∣ r ∣$

$2∣ r ∣$

Given, $∣ u ∣ = ∣ v ∣ = 1$
and $u . v = 0$
ie, angle between
$u$ and $v$ is $90^{o}$
$∴$ $∣ u \times v ∣ = ∣ u ∣∣ v ∣ sin θ = 1$

Q. u^ and v^ are unit vectors such that u^.v^=0 . If r is any vector coplanar with u and v then the magnitude of the vector r×(u^×v^) is :

0

1

∣r∣

2∣r∣

Given, ∣u∣=∣v∣=1 and u.v=0 ie, angle between u and v is 90o ∴ ∣u×v∣=∣u∣∣v∣sinθ=1

Q. $\overset{u}{^}$ and $\overset{v}{^}$ are unit vectors such that $\overset{u}{^} . \overset{v}{^} = 0$ . If $r$ is any vector coplanar with $u$ and $v$ then the magnitude of the vector $r \times (\overset{u}{^} \times \overset{v}{^})$ is :

$0$

$1$

$∣ r ∣$

$2∣ r ∣$

Given, $∣ u ∣ = ∣ v ∣ = 1$
and $u . v = 0$
ie, angle between
$u$ and $v$ is $90^{o}$
$∴$ $∣ u \times v ∣ = ∣ u ∣∣ v ∣ sin θ = 1$