Question

The value of p for which vectors `hati + 2hatj + 3hatk and 2hati - phatj + hatk` are perpendicular to each other is ______.

Options

• 0

• 1

• `5/2`

• `-5/2`

Answer 1

The value of p for which vectors `hati + 2hatj + 3hatk and 2hati - phatj + hatk` are perpendicular to each other is `underlinebb(5/2)`.

Explanation:

For perpendicular vectors, the dot product is zero:

1 × 2 + 2(−p) + 3 ⋅ 1 = 0

⇒ 2 − 2p + 3 = 0

Thus, 5 − 2p = 0

⇒ p = `5/2`

Hence, vectors are perpendicular for this value.