Advertisements
Advertisements
Question
Given a + b + c + d = 0, state whether the following statement is correct or incorrect:
The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
Options
Correct
Incorrect
Advertisements
Solution
This statement is correct.
Explanation:
The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
∴ a + b + c + d = 0
∴ |a| = |b + c + d|
But |b + c + d| ≤ |b| + |c| + |d|
∴ |a| ≤ |b| + |c| + |d|
APPEARS IN
RELATED QUESTIONS
Given a + b + c + d = 0, state whether the following statement is correct or incorrect:
b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear.
Establish the following vector inequalities geometrically or otherwise:
- | a+b | ≤ |a| + |b|
- |a + b| ≥ | |a| - |b| |
- |a - b| ≤ |a| + |b|
- |a-b| ≥ | |a| - |b| |
When does the equality sign above apply?
Given a + b + c + d = 0, state whether the following statement is correct or incorrect:
The magnitude of (a + c) equals the magnitude of (b + d).
The resultant of two vectors `vecA` and `vecB` is `vecC`. If the magnitude of `vecB` is doubled, the new resultant vector becomes perpendicular to `vecA`, then the magnitude of `vecC` is
For two vectors A and B, A + B = A − B is always true when
- |A| = |B| ≠ 0
- A ⊥ B
- |A| = |B| ≠ 0 and A and B are parallel or anti parallel
- When either |A| or |B| is zero
What is the essential condition required for two or more vectors to be added or subtracted?
A boat is moving upstream against a current. This is an example of which type of vector combination?
When two anti-parallel vectors are combined, the direction of the resultant is:
Multiple engines pushing an aircraft forward is an example of:
A swimmer attempts to swim upstream. The swimmer can swim at 4 m/s in still water, but the current flows downstream at 1.5 m/s. What is the swimmer's net velocity relative to the ground?
Vector subtraction is______.
The resultant of two vectors will be maximum, if they are ______.
The resultant of two vectors will be minimum, if they are ______.
If more than three forces are acting on a heavy rigid body such that the body is in balanced state, then all the forces are ______.
If the sum of two unit vectors is a unit vector, then magnitude of difference is ______.
