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9 سوالات: ای کیٹ ریاضی، جوابات اور وضاحت کے ساتھ۔
What is the distance between the points (1, 2) and (4, 6)?
What is the slope of the line through (1, 2) and (3, 8)?
Which is the equation of a circle with centre at the origin and radius 5?
درست جواب: x^2 + y^2 = 25
A circle with centre (0, 0) and radius r has the equation x^2 + y^2 = r^2.
What is the midpoint of the points (2, 4) and (6, 10)?
درست جواب: (4, 7)
The midpoint is ((2 + 6) / 2, (4 + 10) / 2) = (4, 7).
What is the dot product of the vectors (1, 2, 3) and (4, -5, 6)?
What is the magnitude of the vector (3, 4)?
What is i x j, the cross product of the unit vectors i and j?
What is the focus of the parabola y^2 = 8x?
درست جواب: (2, 0)
Comparing with y^2 = 4ax gives 4a = 8, so a = 2 and the focus is (2, 0).
Two vectors are perpendicular when their dot product is:
درست جواب: 0
a . b = |a||b| cos(theta), which is 0 exactly when the angle is 90 degrees.