Vector $\to A$ of magnitude 4 units is directed along the positive x-axis. Another vector $\to B$ of magnitude 3 units lies in the x-y plane and makes an angle $30^{\circ}$ with the positive x-axis as shown in the figure. Then $\to A . \to B$ is

Q. A vector in xy - plane has a magnitude of

25 m

and magnitude of x - component is

20 m

. The angle it makes with the positive x - axis is

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If vector ¯¯¯¯¯¯¯¯OP in XY plane whose magnitude is √3 makes an angle 60o with Y-axis, the length of the component of the vector in the direction of X-axis is

The correct option is D 32As angle of vector with X-axis is complimentary with angle with Y-axis, therefore, angle of vector with X-axis =30oComponent of vector with X-axis =|OP|cos30=√3×√32=32

If vector $¯ ¯¯¯¯¯¯ ¯ O P$ in XY plane whose magnitude is $\sqrt{3}$ makes an angle $60^{o}$ with Y-axis, the length of the component of the vector in the direction of X-axis is

The correct option is D $\frac{3}{2}$
As angle of vector with X-axis is complimentary with angle with Y-axis, therefore, angle of vector with X-axis $= 30^{o}$
Component of vector with X-axis $= | O P | cos 30 = \sqrt{3} \times \frac{\sqrt{3}}{2} = \frac{3}{2}$