Question 54 of 68beginner🔧 ApplyNumerical1 mark

Find the value of x for which x(î + ĵ + k̂) is a unit vector.

Correct Answer

x = ± 1/3\sqrt{3}

Exercise: MISCELLANEOUS EXERCISE ON CHAPTER 10 | Q: 5 | (Page 35)
For More Understanding

Explanation

The question requires finding the scalar value x such that the vector x(î + ĵ + k̂) has magnitude 1. From the context, Example 6 shows that the magnitude of a vector is found using the formula |a⃗| = coefficientofı^\sqrt{coefficient of î}² + (coefficient of ĵ)² + (coefficient of k̂)². The magnitude of the unit vector must equal 1.

Solution Steps

  1. Step 1: Let the given vector be a⃗ = x(î + ĵ + k̂) = xî + xĵ + xk̂

  2. Step 2: For a unit vector, |a⃗| = 1

  3. Step 3: Calculate magnitude: |a⃗| = x\sqrt{x}² + (x)² + (x)² = 3x2\sqrt{3x²} = |x|3\sqrt{3}

  4. Step 4: Set |x|3\sqrt{3} = 1

  5. Step 5: Therefore, |x| = 1/3\sqrt{3}, giving x = ± 1/3\sqrt{3}

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