Question

Show that a=i-j/√2 is a unit vector

Answer 1

we know, magnitude of unit vector equals one.

so, given vector will be a unit vector when its magnitude will be one or 1.

here, a = (i -j)√2

⇒a = (1/√2)i + (-1/√2)j

we know, if any vector , A = x i + yj are given then magnitude of A = |A| = √{x² + y²}

so, magnitude of a = |a| = √{(1/√2)² + (-1/√2)²}

= √{1/2 + 1/2} = √1 = 1

hence, magnitude of a = |a| = 1

so, it is clear that a = (i - j)/√2 is a unit vector .

Answer 2

Answer:

so, given vector will be a unit vector when its magnitude will be one or 1.

here, a = (-)√2

→ a = (1/√/2)+(-1/√2)j

we know, if any vector, Axi + yj are given then magnitude of A= IAI = √(x² + y²)

so, magnitude of a = lal = √((1/√2)² + (-1/√2)³)

= √{1/2 + 1/2} = √1=1

hence, magnitude of a = lal=1

so, it is clear that a = (i - j)/√2 is a unit vector.

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