Topic Details (Notes format)

How to Solve Basic Vector Problems (2D)

Subject: Mathematics

Book: Maths Mastery

Vector problems revolve around magnitude and direction. For example, if u20d7A=[2,3], its magnitude is √(2²+3²)=√13. Adding vectors u20d7A+u20d7B sums components: [a₁+b₁, a₂+b₂]. Dot product u20d7A · u20d7B = a₁b₁+a₂b₂. These operations appear in physics (force or velocity decomposition), game development (movement), or 2D geometry transformations. Building comfort with 2D vectors paves the way for 3D expansions, fosters strong geometric intuition, and is essential for multi-dimensional problem-solving across STEM fields.

Practice Questions

If x:y = 2:3 and z:y = 4:3, what is x:z?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If the radius of a circle is 7 cm, what is its circumference?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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What is the cube root of 729?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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