Question

pls tell the answers

Answer 1

Answer:

The dot product of Perpendicular vector must be equal to zero.

Let's check the option one by one which satisfy the above condition.

Option (I)

$\longrightarrow \tt (\hat{i} + \hat{j} + \hat{k} ).(\hat{i} - \hat{j} + \hat{k} ) = 0$

$\longrightarrow \tt1 - 1 + 1 = 0$

$\longrightarrow \tt 1 \neq 0$

Option (ii)

$\longrightarrow \tt(\hat{i} + \hat{j} + \hat{k} ).(3\hat{i} + 2 \hat{j} - 5 \hat{k} ) = 0$

$\longrightarrow \tt3 +2 - 5 = 0$

$\longrightarrow \tt5 - 5 = 0$

$\longrightarrow \tt0= 0$

Option (iii)

$\longrightarrow \tt(\hat{i} + \hat{j} + \hat{k} ).( - \hat{i} - \hat{j} - \hat{k} ) = 0$

$\longrightarrow \tt - 1 - 1 - 1= 0$

$\longrightarrow\tt- 2 - 1= 0$

$\longrightarrow \tt- 3 \neq 0$

Option (iv)

$\longrightarrow \tt(\hat{i} + \hat{j} + \hat{k} ).( - 3\hat{i} + 2 \hat{j} -5 \hat{k} ) = 0$

$\longrightarrow \tt - 3 + 2 - 5 = 0$

$\longrightarrow \tt- 1 - 5 = 0$

$\longrightarrow \tt- 6 \neq0$

By observing the above options we clearly see that only option (ii) is satisfying the given condition.

Hence, the option (ii) is correct.