30 Questions
What is the magnitude of the vector a × b?
|a||b|sinθ
What is the direction of the vector a × b?
Perpendicular to the plane of a and b
If a and b are two vectors, what is the relation between a × b and b × a?
a × b = -b × a
If a and b are two vectors, and m is a scalar, what is the relation between ma × b and a × mb?
ma × b = a × mb
What is the property of vector product that states a × (b + c) = a × b + a × c?
Distributivity
What is the primary characteristic of a scalar quantity?
It has only magnitude and no direction
What is the term used to describe the line of unlimited length of which a vector AB is a segment?
Support
Which of the following is an example of a vector quantity?
Displacement
What is the magnitude of a vector denoted by?
| a |
What is the name of the point from which a vector begins?
Initial point
According to the triangle law of vector addition, what does the third side of the triangle represent?
The sum of the two vectors
What is the modulus of a vector m a, where a is a non-zero vector and m is a non-zero scalar?
|m| |a|
If r = 3i - 4j + 5k, what is the direction cosine of r with respect to the x-axis?
3/5
What is the condition for two vectors a and b to be added using the parallelogram law of addition?
They must be represented by adjacent sides of a parallelogram
What is the property of vector addition known as, when the order of the vectors being added does not change the result?
Commutative property
What is the condition for the vectors a and b to be expressed as linear combinations of three non-coplanar vectors?
a and b are non-collinear
What is the result of the vector product (a × b) × (c × d) when a, b, c, and d are vectors?
a vector
What is the angle between two planes P1 and P2, determined by the vectors a, b and c, d, respectively, when (a × b) × (c × d) = 0?
0
What is the expression for an unknown vector r, when a, b are two known non-collinear vectors?
r = x a + y b + z (a × b)
What is the term used to describe the process of finding an unknown vector or a number of vectors satisfying a given condition?
Solving a vector equation
What is the number of non-coplanar vectors that can be formed from two known non-collinear vectors a and b?
3
What is the condition for two vectors a and b to be parallel?
a × b = 0
What is the expression for the vector product of two vectors a and b?
a × b
What is the name of the method used to add two vectors a and b, when the third side of the triangle represents the resultant vector?
Parallelogram law of vector addition
What is the result of the vector equation (a × b) × (c × d) = 0, when a, b, c, and d are vectors?
a × b is parallel to c × d
What is the condition for two vectors a and b to be equal?
They have the same or parallel support and the same sense.
What is the reciprocal of a vector?
A vector having the same direction as the given vector but magnitude equal to the reciprocal of the given vector.
What is a localized vector?
A vector which is drawn parallel to a given vector through a specified point in space.
What is a free vector?
A vector which is independent of its position in space.
What is the position vector of a point A?
The vector OA which represents the position of the point A with respect to a fixed point O.
Test your understanding of vector algebra concepts, including the cross product of two vectors, its relation to the area of a parallelogram, and vector notation. Practice problems and formulas to help you master vector algebra.
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