Question

A unit vector a makes an angle π / 4 with z-axis. If a + i + j is a unit vector, then a is equal to

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Answer 1

✔ Explanation :-

✔ Solution :-

Let a = li + mj + nk, where l² + m² + n² = 1. a makes an angle π / 4 with z−axis.

=> Hence, n = 1 / √2, l² + m² = 1 / 2 …..(i)

=> Therefore, a = li + mj + k / √2

=> a + i + j = (l + 1) i + (m + 1) j + k / √2

Its magnitude is 1, hence (l + 1)² + (m + 1)² = 1/2...(ii)

From (i) and (ii),

=> 2lm = 1 / 2

=> l = m = −1 / 2

=> a = [−i / 2] − [j / 2] + [k / √2].

Hence,

• The value of a is [−i / 2] − [j / 2] + [k / √2].

Answer 2

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Let a = li + mj + nk, where l² + m² + n² = 1. a makes an angle π / 4 with z−axis.

→ Hence,n = 1/√2, l² + m² = 1/2 Equation(i)

→ Therefore, a = li + mj + k/√2

→ a + i + j = (l + 1) i + (m + 1) j + k/√2

Its magnitude is 1

Hence, (l + 1)² + (m + 1)² = 1/2 Equation (ii)

From Equation (i) & (ii)

→ 2lm = 1/2

→ l = m = −1/2

→ a = [−i /2] − [j/2] + [k/√2].

Hence, the value of a is [−i/2] − [j/2] + [k/√2].

Hope it Helps Buddy ♥️

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