In the figure shown a cube of side length a. If OP ⋅ OM = ka 2, find the value of k

Question

In the figure shown a cube of side length a. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/3f662d9bcbc29ad613fa6325b9aa27fc-.png" /> If OP ⋅ OM = ka 2, find the value of k (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

OP =a hat i + hat j + a hat k OM = ai +a hat k OP ⋅ OM =2 a 2 ⇒ hat k =2

Q. In the figure shown a cube of side length $a$ .

If $OP \cdot OM = k a^{2}$ , find the value of $k$

$OP = a \hat{i} + \hat{j} + a \hat{k}$
$OM = ai + a \hat{k}$
$OP \cdot OM = 2 a^{2}$
$\Rightarrow \hat{k} = 2$

Q. In the figure shown a cube of side length a. If OP⋅OM=ka2, find the value of k

OP=ai^+j^​+ak^ OM=ai+ak^ OP⋅OM=2a2 ⇒k^=2

Q. In the figure shown a cube of side length $a$ .

If $OP \cdot OM = k a^{2}$ , find the value of $k$

$OP = a \hat{i} + \hat{j} + a \hat{k}$
$OM = ai + a \hat{k}$
$OP \cdot OM = 2 a^{2}$
$\Rightarrow \hat{k} = 2$