Advertisements
Advertisements
Question
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.
Options
Correct
Incorrect
Advertisements
Solution
This statement is Correct.
Explanation:
∴ a + b + c + d = 0
∴ a + c = (b + d)
∴ b + d = (a + c)
If a + d are not collinear, then a + d will be in the plane of a and d.
Therefore, b + d = -(a + d) will also be in the plane of a + d. If a and d are collinear, then -(a + d) will also be collinear with a and d; therefore, b + c will also be parallel to a and d.
APPEARS IN
RELATED QUESTIONS
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
Given below in column I are the relations between vectors a, b and c and in column II are the orientations of a, b and c in the XY plane. Match the relation in column I to correct orientations in column II.
| Column I | Column II | ||
| (a) | a + b = c | (i) |  |
| (b) | a – c = b | (ii) |  |
| (c) | b – a = c | (iii) |  |
| (d) | a + b + c = 0 | (iv) |  |
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?
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 process of finding the resultant of two or more vectors is called ______.
The resultant of two vectors will be maximum, if they are ______.
The resultant of two vectors will be minimum, if they are ______.
The process of finding the components of a given vector is called as ______.
If the sum of two unit vectors is a unit vector, then magnitude of difference is ______.
A vector \[\vec a\] is turned without a change in its length through a small angle dθ. The value of |Δ\[\vec a\]| and Δa are respectively
