If two non-zero vectors u and v are perpendicular (orthogonal), what is the value of their dot product u . v?
Answer and explanation
Correct answer: B. 0
- Step 1: The dot product formula is u . v = ||u|| ||v|| cos(theta).
- Step 2: When vectors are perpendicular, the angle theta = 90 degrees (pi/2 radians), and cos(90 degrees) = 0. Therefore, u . v = 0.
Answer
0.
Why not the others: '1' is the dot product of two identical normalized unit vectors; '-1' occurs when vectors are anti-parallel; '||u|| * ||v||' occurs when vectors are parallel in the same direction.
Practise more Vectors, Trigonometry and Analytic Geometry.
Free questions with an explanation for every one, and full timed Tawjihiya Bahrain (Secondary School Certificate) mock tests.
More Vectors, Trigonometry and Analytic Geometry questions
- Find the magnitude of the 3D vector v = 3i - 4j + 12k.
- Calculate the dot product (scalar product) of vectors u = (2, -3, 5) and v = (4, 1, -2).
- Find the center and radius of the circle with equation x^2 + y^2 - 6x + 8y = 0.
- What is the exact value of sin(15 degrees)?
- Simplify the trigonometric expression: cos(2theta) + 2sin^2(theta).
- Find the cross product u x v of vectors u = (1, 0, 0) and v = (0, 1, 0).