Under what condition the direction of the sum and difference of two vectors will be the same?

Hence the direction of sum and difference of two vectors will remain the same as long as the two vectors are of different magnitude, acting in the same direction. And the difference should be taken such that the vector with less magnitude should be subtracted from the vector with greater magnitude.

What happens if two vectors are perpendicular to each other?

If two vectors are perpendicular to each other, then their dot product is equal to zero.

When given two perpendicular vectors that are added together what should you use to determine the magnitude of the resultant vector?

Since the northward displacement and the eastward displacement are at right angles to each other, the Pythagorean theorem can be used to determine the resultant (i.e., the hypotenuse of the right triangle). The result of adding 11 km, north plus 11 km, east is a vector with a magnitude of 15.6 km.

How do you prove that vector A and vector B are parallel?

Find the cross products of the two vectors, if the cross product is equal to zero then the given 2 vectors are parallel otherwise not. You can also use the condition that two vectors are parallel if and only if they are scalar multiples of one another otherwise they are not parallel.

Can two vectors with different magnitudes be combined to give a zero resultant?

Two vectors of different magnitudes cannot add to give zero resultant. Three vectors of different magnitude can add to give zero resultant if they are copanar.

How do you know if two vectors are perpendicular?

Two vectors are perpendicular if their dot product is zero, and parallel if their dot product is 1. Take the dot product of our two vectors to find the answer: Using our given vectors: Thus our two vectors are perpendicular.

Is the sum of two vectors equal to their difference?

The sum of two vectors is at right angles to their difference. How do you show that the vectors are equal in magnitude? Let’s say we have two vectors, v= (a, b, c) and w= (d, e, f).

What is the magnitude of the resultant of two equal vectors?

We are given A = B= R=A (say), then So if two equal vectors are at 120° to each other the magnitude of the resultant is equal to either vector. The sum of two vectors is at right angles to their difference. How do you show that the vectors are equal in magnitude?

How do you find the magnitude of a right angle vector?

R² = A ² + B² + 2 AB Cos ß, where ß is the angle between the vectors A,B. We are given A = B= R=A (say), then So if two equal vectors are at 120° to each other the magnitude of the resultant is equal to either vector. The sum of two vectors is at right angles to their difference.