Question 24 of 68intermediate🔧 ApplyNumerical2 marks

Find the projection of the vector î + 3ĵ + 7k̂ on the vector 7î - ĵ + 8k̂.

Correct Answer

The projection of the vector î + 3ĵ + 7k̂ on the vector 7î - ĵ + 8k̂ is 60/114\sqrt{114}.

Exercise: EXERCISE 10.3 | Q: 4 | (Page 24)
For More Understanding

Explanation

This question tests the concept of projection of one vector onto another. According to Example 16 in the textbook, the projection of vector a on vector b is given by (a · b)/|b|. The student needs to apply the dot product formula and calculate the magnitude of the second vector.

Solution Steps

  1. Step 1: Let a = î + 3ĵ + 7k̂ and b = 7î - ĵ + 8k̂

  2. Step 2: Find the dot product a · b = (1)(7) + (3)(-1) + (7)(8) = 7 - 3 + 56 = 60

  3. Step 3: Find the magnitude |b| = 72+(−1\sqrt{7² + (-1}² + 8²) = 49+1+64\sqrt{49 + 1 + 64} = 114\sqrt{114}

  4. Step 4: Apply the projection formula: Projection of a on b = (a · b)/|b| = 60/114\sqrt{114}

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