For what value of k are the vectors u = <2, k, -3> and v = <6, 4, 2> orthogonal (perpendicular)?
Answer and explanation
Correct answer: C. -1.5 (or -3/2)
- Step 1: Two vectors are orthogonal if and only if their dot product equals zero: u . v = 0.
- Step 2: Compute u . v: (2)(6) + (k)(4) + (-3)(2) = 12 + 4k - 6 = 6 + 4k.
- Step 3: Set to zero: 6 + 4k = 0 => 4k = -6 => k = -6/4 = -1.5.
Answer
-1.5 (or -3/2).
Why not the others: '3' sets 6 - 4k = 0; '0' ignores the constant term; '-6' fails to divide by the coefficient 4.
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