Let \to ^ ^ ^ a = 3 i - j + 2k, \to ^ ^ b = a \times ( i - 2k) and \to ^ c = b \times k . Then the projection of \to ^ c - 2j \to is : on a
Step-by-Step Solution
Key Concept: Apply the core result for dot product, cross product and projections and simplify using the given constraints.
b = \to ^ ^ a \times ( i - 3k) (1) ∣^ i ^ j ^ k ∣ ∣ ∣ ^ ^ ^ = ∣3 -1 2 ∣ = 2i + 8j + k ∣ ∣ ∣1 0 -2 ∣ \to \to ^ ^ ^ c = b \times k = 8i - 2j \to ^ ^ ^ c - 2j = 8i - 4j \to Projection of (^i - 2^j) on a ⟨8, -4, 0⟩ ⋅ ⟨3, -1, 2⟩ \to ^ ( c - 2j) ⋅ ^ a = \sqrt14 28 = = 2\sqrt14 \sqrt14
Correct Answer: 1