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Quantities with a magnitude and a direction are known as vector quantities. If we consider force as an example, we may express it in terms of its magnitude and direction. In physics, such quantities are known as vector quantities. When it comes to temperature, we can grasp its magnitude (for example, 100°C), but not its direction. Scalar quantities are the name for these sorts of quantities. The definition and kinds of vectors are discussed in this article. The term “vector” refers to a quantity that has both a magnitude and a direction. It is beneficial to the study of motion. Vector quantities are represented by an arrow with the same direction as the quantity and a length proportionate to the magnitude of the quantity.
- Two vectors are perpendicular to each other: 2i^+3j^+8k^ and 4i^-4j^+ak^. What is the value of a?
(a) -½
(b) ½
(c) 1
(d) -1
Answer- b, a.b =|a| |b| cosθ used to find the result.
- A force of 50 N operates on a body, displacing it across a distance of 10 meters in a direction where the force forms a 60-degree angle with the body. What is the work done?
(a) 100 J
(b) 150 J
(c) 200 J
(d) 250 J
Answer- d.
- If the difference between two vectors is perpendicular to their total. The magnitude ratio will be
(a) 1
(b) 2
(c) 3
(d) 4
Answer- a.
- If A . B = A x B, the angle between A and B will be-
(a) π
(b) π/2
(c) π/3
(d) π/4
Answer- d.
- What is the area of the parallelogram whose vectors P =2i+3j and Q =i+4j represent?
(a) 5 Units
(b) 10 Units
(c) 15 Units
(d) 20 Units
Answer- a, area of parallelogram =| a × b |.
- What is the angle formed by the vectors A B and B A?
(a) π
(b) 00
(c) π/2
(d) π/4
Answer- a.
- The angle formed by A +B and A- B is –
(a) π
(b) π/2
(c) π/4
(d) 0
Answer- b .
10. The magnitude of a unit vector is-
(a) 5
(b) 1
(c) 10
(d) 0.
Answer- b, as unit vector mean vector whose value is 1.
- What occurs when you multiply a vector by a scalar?
(a) The magnitude of it is multiplied by that much.
(b) Its direction rotates by that amount in the XY plane.
(c) Its direction rotates by that amount in the YZ plane.
(d) Its direction rotates by that much in the ZX plane.
Answer- a.
12. A automobile drives 5 meters in the X direction, then 7 meters in the Y direction. What is the car’s final vector location with relation to the origin?
(a) 5î + 7ĵ
(b) 7î + 5ĵ
(c) 7î + 7ĵ
(d) 5î + 5ĵ
Answer- a.
13. What is the result of multiplying î + 14 by √49?
(a) 7î + 98ĵ
(b) 98î + 14ĵ
(c) 7î + 98ĵ
(d) (î + 7ĵ)*√49
Answer- a, simple multiplication is performed here.
- When you multiply 2î + 7ĵ by 5, you get –
(a) 10î + 35ĵ
(b) 2î + 35ĵ
(c) 10î + 7ĵ
(d) 2î + 7ĵ
Answer- a, simple multiplication is performed here.
15.If you divide 5 î + 10ĵ by 5, you get-
(a) î + 2ĵ
(b) î + 4ĵ
(c) î + ĵ
(d) 2î + ĵ,
Answer- a, simple division is performed here.
16. When you add 11 times the unit vector along X to 7 times the unit vector along Y, you get _____
(a)11î + 7ĵ
(b) 7î + 11ĵ
(c) 7î + 7ĵ
(d) 11î + 11ĵ
Answer- a.
- A cross product is a mathematical process that takes place between-
(a) 2 scalar numbers
(b) a scalar and a vector
(c) 2 vectors
(d) any 2 numbers
Answer- c , cross product is a mathematical operation that is done on two vectors in a three-dimensional plane. It has a wide range of applications in physics and computer programming.
18. What is another name for a cross product?
(a) scalar product
(b) vector product
(c) dot product
(d) multiplication
Answer- b, cross product is often referred to as a vector product. It is a mathematical operation that is carried out on two vectors in a three-dimensional plane.
- What is the size of the resultant of two parallel vectors a and b’s cross product?
(a) |a|.|b|
(b) |a|.|b| cos(180)
(c) |a|.|b| sin(180)
(d) 1
Answer- c, because the angle between two parallel vectors is 0 or 180 degrees, the consequent of their cross product is always 0. As a result, the answer is |a|.|b| sin (180).
- What is the general formula for calculating the magnitude of the cross product of two vectors with an angle between them?
(a) |a|.|b|
(b) |a|.|b| cos(θ)
(c) |a|.|b| sin(θ)
(d) |a|.|b| tan(θ)
Answer- c, as |a|.|b| sin(θ) is the generic formula for calculating the magnitude of the cross product of two vectors. It has a perpendicular orientation to the plane containing a and b.
- In the realm of computer graphics, the notion of cross product is used.
(a) true
(b) false
Answer- a, in the realm of computer graphics, the idea of cross product is used. It may be used to determine how a polygon winds around a point.
22. Which of the following equals a x b (two vectors)?
(a) – (a x b)
b) a.b
(c) b x a
(d) – (b x a)
Answer- d, the a x b vector product equals – (b x a). These vectors have opposing directions, as shown by the negative sign.
23. What may the cross product of two vectors be used for?
(a) area of rectangle
(b) area of square
(c) area of parallelogram
(d) perimeter of rectangle
Answer-c, the area of a parallelogram may be calculated by taking the cross product of two vectors. To do so, we must think of the vectors as the parallelogram’s neighbouring sides.
