1.

the vector Q which has a magnitude of 8 is added to the vector P which lies along the x-axis. the resultant of these vectors is third vector R,which lies along the y-axis and has magnitude twice that of P. the magnitude of P is?

Answer»

Let the magnitude of the Vector P be a.

∴ In Vector Form,

\hat{i}Vector P = a

Let the magnitude of Vector R be r.

∴ r = 2a

In Vector Form,

\hat{R}\hat{j} = 2a

Now, We know,

\hat{R}\hat{P}\hat{Q} = +

⇒ |R²| = |P|² + |Q|² + 2 |PQ| Cosθ

Cos θ = 90° [Angle between the x-y axis is 90°]

⇒ |R²| = |P|² + |Q|² + 2 |PQ|

∴ (2a)² = (a)² + (8)² + 2(a)(8)

⇒ 4a² = a² + 64 + 16a

⇒ 3a² - 16a - 64 = 0

∴ 3a² - 24A + 8A - 64 = 0

⇒ 3a(a - 8) + 8(a - 8) = 0

∴ (a - 8)(3a + 8) = 0

⇒ a = 8 and a = -8/3

a ≠ -8/3.

Hence, the Magnitude of the Vector P is 8.

Hope it helps.


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