Question 31 of 68intermediate🔧 ApplyMCQ1 mark

If a⃗ is a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λa⃗ is unit vector if

Exercise: EXERCISE 10.3 | Q: 18 | (Chapter: 25)
For More Understanding

Explanation

Option D is correct. According to the textbook, the magnitude of vector λa⃗ is given by |λa⃗| = |λ||a⃗|. For λa⃗ to be a unit vector, its magnitude must equal 1. Since |a⃗| = a (given), we have |λa⃗| = |λ|·a = 1. Solving for a gives a = 1/|λ|. The textbook also confirms this by showing that if λ = 1/|a|, then |λa⃗| = 1, which is equivalent to saying a = 1/|λ|.

Solution Steps

  1. Step 1: For λa⃗ to be a unit vector, we need |λa⃗| = 1

  2. Step 2: Using the formula from context: |λa⃗| = |λ||a⃗| = |λ|·a

  3. Step 3: Setting this equal to 1: |λ|·a = 1

  4. Step 4: Solving for a: a = 1/|λ|

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