JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Vector

Two forces

F_{1}

and

F_{2}

are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between

F_{1}

and

F_{2}

cos^{- 1} (\frac{1}{n})

. The value of

∣ n ∣

is ______.

Answer: 6

Solution

Let the smaller force be

F

; the larger is

3 F

, and the resultant equals the larger force,

R = 3 F

R^{2} = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} cos θ

(3 F)^{2} = F^{2} + (3 F)^{2} + 2 (F) (3 F) cos θ

9 F^{2} = 10 F^{2} + 6 F^{2} cos θ \Rightarrow cos θ = - \frac{1}{6} .

Writing

θ = cos^{- 1} (\frac{1}{n})

gives

\frac{1}{n} = - \frac{1}{6}

, so

n = - 6

and

∣ n ∣ = 6

.
Answer: 6.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Vector →

More JEE Main questions on Vector

When the position vector $r = x \hat{i} + y \hat{j} + z \hat{k}$ changes sign as $- r$ , which one of the following vector will not flip under sign change ?
JEE Main 2026View solution →
Two particles are located at equal distance from origin. The position vectors of those are represented by $A = 2 \hat{i} + 3 n \hat{j} + 2 \hat{k}$ and $B = 2 \hat{i} - 2 \hat{j} + 4 p \hat{k}$ , respectively. If both the vec …
JEE Main 2025View solution →
A particle moves in $x - y$ plane under the influence of a force $F$ such that its linear momentum is $P (t) = \hat{i} cos (kt) - \hat{j} sin (kt)$ . If k is constant, the angle between …
JEE Main 2024View solution →
The angle between vector $Q$ and the resultant of $(2 Q + 2 P)$ and $(2 Q - 2 P)$ is:
JEE Main 2024View solution →
For three vectors $A = (- x \hat{i} - 6 \hat{j} - 2 \hat{k})$ , $B = (- \hat{i} + 4 \hat{j} + 3 \hat{k})$ and $C = (- 8 \hat{i} - \hat{j} + 3 \hat{k})$ , if $A \cdot (B \times C) = 0$ , then value of x is ______.
JEE Main 2024View solution →
Three vectors $OP$ , $OQ$ and $OR$ each of magnitude A are acting as shown in figure. The resultant of the three vectors is $A x$ . The value of x is ____.
JEE Main 2024View solution →