Question

Show that vector a = (vector i - vector j)/√2 is a unit vector.​

Answer 1

Explanation ⇒ To prove that,

$\frac{\hat{i} - \hat{j}}{\sqrt{2} }$ is an unit vector. means its magnitude is 1.

Okay. For magnitude, first separate x term and y terms.

Thus, i/√2 - j/√2 = t  (let)

∴ |t|² = (1/√2)² + (-1/√2)²

∴ |t|² = 1/2 + 1/2

∴ |t|² = 1

∴ |t| = 1    [Mod cannot be -ive.]

Hence Proved that given expression is the unit vector having magnitude 1.

Hope it helps.

Answer 2

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$