Perpendicular & parallel vectors
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Flip to reveal answersWhen are two vectors perpendicular?
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All 8 Flashcards — Perpendicular & parallel vectors
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Question
When are two vectors perpendicular?
Answer
When their dot product is 0 (because v·w = |v||w|cos 90° = 0).
Question
When are two vectors parallel?
Answer
When one is a scalar multiple of the other: v = t w (components in the same ratio).
Question
a = (3, k, 2), b = (1, −4, 5) are perpendicular. Find k.
Answer
a·b = 3 − 4k + 10 = 0 ⇒ k = 13/4.
Question
Test: are (6, −9) and (2, −3) parallel?
Answer
Yes — (6, −9) = 3(2, −3), a scalar multiple.
Question
What angle do parallel vectors make? Perpendicular?
Answer
Parallel: 0° (same way) or 180° (opposite). Perpendicular: 90°.
Question
A vector perpendicular to (3, 4) in 2-D?
Answer
Swap and negate one entry: (−4, 3) (or (4, −3)); check (3)(−4)+(4)(3)=0.
Question
How do you find an unknown component for perpendicular vectors?
Answer
Set the dot product equal to 0 and solve the resulting equation for the unknown.
Question
If u = t v, what does that tell you about u and v?
Answer
They are parallel (u is a scaled copy of v).
Read the notes
Full study notes for Perpendicular & parallel vectors
Topic 3.13 hub
Scalar product (HL only)
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