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How do you prove using a diagram that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitude of the two vectors?
You could draw a circle [center at origin] with radius of (a + b), for the two magnitudes a and b. This represents the sum of the magnitudes. Then draw one of the vectors starting at the origin [suppose it's vector a], and then draw a circle centered at the endpoint of vector a, with a radius of b. Drawing a circle demonstrates how the second vector can point in any direction relative to the first vector. The distance from the origin to a point on this second circle is the magnitude of the resultant vector. Graphically this second circle will be entirely inside the first circle and touching it at just one point. Since it lies within the first circle, the distance from the origin to a point on that circle will be less than or equal to the radius of the first circle.
What else can I help you with?
How do you prove three vectors are equal to zero?
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
How do you prove that the diagonals of a rectangle are congruent using vectors?
If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
How do you Prove De Morgans law through Venn diagram overlapping sets?
using ven diagram prove de morgans law
How do you prove that a trapezoid is isosceles?
You prove that the two sides (not the bases) are equal in length. Or that the base angles are equal measure.
How do you prove three vectors are equal to zero?
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
Prove that two vectors must have equal magnitude if their sum is perpendicular to their difference?
Suppose the condition stated in this problem holds for the two vectors a and b. If the sum a+b is perpendicular to the difference a-b then the dot product of these two vectors is zero: (a + b) · (a - b) = 0 Use the distributive property of the dot product to expand the left side of this equation. We get: a · a - a · b + b · a - b · b But the dot product of a vector with itself gives the magnitude squared: a · a = a2 x + a2 y + a2 z = a2 (likewise b · b = b2) and the dot product is commutative: a · b = b · a. Using these facts, we then have a2 - a · b + a · b + b2 = 0 , which gives: a2 - b2 = 0 =) a2 = b2 Since the magnitude of a vector must be a positive number, this implies a = b and so vectors a and b have the same magnitude.
How do you prove that the diagonals of a rectangle are congruent using vectors?
If the vectors emanting from one corner of the rectangel are called a and b then. (a) + (b) = one diagonal (a) + (-b) = the other diagonal and |(a) + (b)| = |(a) + (-b)| (the absolute value of the diagonal's scalars are equal)
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
How do you Prove De Morgans law through Venn diagram overlapping sets?
using ven diagram prove de morgans law
How do you prove that a trapezoid is isosceles?
You prove that the two sides (not the bases) are equal in length. Or that the base angles are equal measure.
Prove that if magnitude of vector A is constant then d by dt of vector A is perpendicular to vector A.?
That is not even true!
How do you prove that 0.999999999999 is equal to one?
You cannot prove that because it's false
Prove that the diagonals of rectangle are equal?
prove any two adjacent triangles as congruent
What is CPCTC used for?
Once you prove that a diagram is congruent then you can say that all the parts are congruent.
How can you prove tha2 equals 1?
It isn't equal, and any proof that they are equal is flawed.
How do you prove De Morgans 2nd law using venn diagram?
To prove De Morgan's second law, which states that the complement of the intersection of two sets is equal to the union of their complements (( (A \cap B)' = A' \cup B' )), we can use a Venn diagram. In the diagram, shade the area representing ( A \cap B ) to show where both sets overlap. The area outside this intersection represents ( (A \cap B)' ), which includes everything outside both ( A ) and ( B ). This shaded area corresponds to the regions of ( A' ) and ( B' ), confirming that ( (A \cap B)' ) indeed equals ( A' \cup B' ).
