You visited us 1 times! Enjoying our articles? Unlock Full Access!

Intro to Torque

The vertices ...

Question

The vertices of a triangle ABC are A(-1, 0, 2), B(1, 2, 0)and C (2, 3, 4). Find (i) vector area of triangle ABC, (ii) the moment of a force of magnitude 10 N acting at A along AB, about C.

5 \sqrt{2}, \frac{10}{\sqrt{3}} \times 5 (- i + j)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 \sqrt{2}, \frac{10}{\sqrt{3}} \times (i - j - 6 k)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 \sqrt{2}, \frac{10}{\sqrt{3}} \times (- i + j + 6 k)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 \sqrt{2}, \frac{10}{\sqrt{3}} \times 5 (i - j)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $5 \sqrt{2}, \frac{10}{\sqrt{3}} \times 5 (i - j)$
$\to A B = \to O B - \to O A = 2 i + 2 j - 2 k$ $\to A C = \to O C - \to O A = 3 i + 3 j + 2 k$
Vector area of $Δ A B C$
$\to A B \times \to A C = ∣ ∣ ∣ ∣ \begin{matrix} i & j & k 2 & 2 & - 2 3 & 3 & 2 \end{matrix} ∣ ∣ ∣ ∣ = 10 i - 10 j$
$∴ Δ = \frac{1}{2} ∣ ∣ ∣ \to A B \times \to A C ∣ ∣ ∣ = 10 \sqrt{2} = 5 \sqrt{2}$
Now unit vector along $A B = \frac{2 i + 2 j - 2 k}{2 \sqrt{3}}$
Hence a force of magnitude 10 N along AB is
$F = \frac{10 (i + j - k)}{\sqrt{3}}$
$∴$ Moment $= r \times F$ ( where
$r = \to C A = - 3 i - 3 j - 2 k)$
$= \frac{10}{\sqrt{3}} ∣ ∣ ∣ ∣ \begin{matrix} i & j & k - 3 & - 3 & - 2 1 & 1 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = \frac{10}{\sqrt{3}} \times 5 (i - j)$

Suggest Corrections

Similar questions

Q. The points

A (2^i -^j +^k), B (^i - 3^j - 5^k)

and

C (3^i - 4^j - 4^k)

represents the vertices of a

△ A B C

. Then

△ A B C

Two forces F1 = (7i + 2j) N and F2 = (-5i + 3j) N act on a particle. The third force F3 that should act on the particle to make it move with constant velocity is a) (2i + 5j) N b) (-2i – 5j) N c) (–2i + 5j) N d) (2i – 5j) N

Q. Arrange the following in ascending order of magnitude

A

: Area of triangle with sides

2^i - 7^j +^k, 4^j - 3^k

B

: Area of triangle with vertices

3^i +^j, 5^i + 2^j +^k,^i - 2^j + 3^k

C

: Area of triangle with vertices

(1, 2, 3)

(2, 5, - 1)

(- 1, 1, 2)

D

: Area of triangle with sides

\to a + 2 \to b

and

2 \to a + \to b

where

| \to a | = 3, | \to b | = 2, (\to a, \to b) = \frac{π}{3}

Q. The adjacent sides

A B

and

A C

of a triangle

A B C

are represented by the vectors

- 2^i + 3^j + 2^k

and

- 4^i + 5^j + 2^k

respectively. The area of the triangle

A B C

is.

Q. The position vectors of the point

A, B

and

C

are

2^i -^j +^k,^i - 3^j - 5^k

and

3^i - 4^j - 4^k .

The greatest angle of triangle

A B C

is.

Join BYJU'S Learning Program