The angle which the vector makes with the y-axis, where and are unit vectors along x- and y-axis, respectively, is
1. cos-1 (3/5)
2. cos-1 (2/3)
3. tan-1 (2/3)
4. sin-1 (2/3)
The components of a vector along the x and y directions are (n + 1) and 1, respectively. If the coordinate system is rotated by an angle θ, then the components change to n and 3. The value of n will be:
1. 2
2. cos 60°
3. sin 60°
4. 3.5
If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:
1. 90°
2. 45°
3. 180°
4. 0°
Six vectors have the directions as indicated in the figure. Which of the following statements may be true?
1.
2.
3.
4.
The projection of a vector on the XY-plane has a magnitude of:
1. \(3\)
2. \(4\)
3.
4.
If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:
1.
2.
3.
4. \(1\)
Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:
1. 12 N, 6 N
2. 13 N, 5N
3. 10 N, 8 N
4. 16 N, 2 N
Assertion (A): | The graph between P and Q is a straight line when P/Q is constant. |
Reason (R): | The straight-line graph means that P is proportional to Q or P is equal to a constant multiplied by Q. |
Which one, of the following statements, is correct?
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False |
Given that makes an angle . Which of the following options is correct?
1.
2.
3.
4.
Two forces, 1 N and 2 N, act along with the lines x = 0 and y = 0. The equation of the line along which the resultant lies is given by:
1. y - 2x = 0
2. 2y - x = 0
3. y + x = 0
4. y - x = 0