If $\to i, \to j, \to k$ be the position vectors of the vertices of a triangle, then its area is

\sqrt{3}

sq. units

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

\frac{1}{2} \sqrt{3}

sq. units

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

3

sq. units

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

3 \sqrt{3}

sq. units

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

Open in App

Solution

The correct option is B $\frac{1}{2} \sqrt{3}$ sq. units
$\to n =^i \times^j +^j \times^k +^k \times^i$
$\to n =^k +^i +^j$
$| \to n | = \sqrt{3}$
Area of $Δ = \frac{1}{2} | \to n |$
$= \frac{\sqrt{3}}{2}$

Suggest Corrections

Similar questions

Q. If

| z_{1} | = | z_{2} | = | z_{3} | = 1

and

z_{1} + z_{2} + z_{3} = 0

, then area of the triangle whose vertices are

z_{1}, z_{2}, z_{3}

Q. If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is

(a) 183 sq. units

(b)

\frac{183}{2}

sq. units

(c) 366 sq. units

(d)

\frac{183}{4}

sq. units

The area of an equilateral triangle with perimeter 18x is:

Q. Let ABC be a triangle of area 24 sq. units and PQR be the triangle formed by the mid-points of the sides of Δ ABC. Then the area of ΔPQR is

(a) 12 sq. units

(b) 6 sq. units

(c) 4 sq. units

(d) 3 sq. units

If the length of each edge of a regular tetrahedron is 'a', then its surface area is
(a) $\sqrt{3} a^{2}$ sq. units
(b) $\frac{\sqrt{3}}{2} a^{2}$ sq. units
(c) $\sqrt{\frac{2}{3}} a^{2}$ sq. units
(d) $\sqrt{6} a^{2}$ sq. units

Join BYJU'S Learning Program

If →i,→j,→k be the position vectors of the vertices of a triangle, then its area is

The correct option is B 12√3 sq. units→n=^i×^j+^j×^k+^k×^i→n=^k+^i+^j|→n|=√3Area of Δ=12|→n|=√32

If $\to i, \to j, \to k$ be the position vectors of the vertices of a triangle, then its area is

The correct option is B $\frac{1}{2} \sqrt{3}$ sq. units
$\to n =^i \times^j +^j \times^k +^k \times^i$
$\to n =^k +^i +^j$
$| \to n | = \sqrt{3}$
Area of $Δ = \frac{1}{2} | \to n |$
$= \frac{\sqrt{3}}{2}$