The vectors from the origin O to the points A and B is A -3 -6 -2 k- and B -2 -2 k- respectively- The area of triangle OAB beA- 5-2-17 sq- unitsB- 4-5-17 sq- unitsC- 0-5-17 sq- unitsD- 0-3-17 sq- units

The correct option is A 52√(17) sq. unitsArea of triangle = 12|(A×B)| = 12|(3î 6ĵ+2k̂) ×(2î+ ĵ 2k̂)| nbsp; = 12× |10î+ 10ĵ + 15k̂| = 52× (√(17)) sq. units ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

The vectors f...

Question

The vectors from the origin $O$ to the points $A$ and $B$ is $\to A = 3^i - 6^j + 2^k$ and $\to B = 2^i +^j - 2^k$ respectively. The area of triangle $O A B$ be

\frac{5}{2} \sqrt{17}

sq. units

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\frac{2}{5} \sqrt{17}

sq. units

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\frac{3}{5} \sqrt{17}

sq. units

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\frac{5}{3} \sqrt{17}

sq. units

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Solution

The correct option is A $\frac{5}{2} \sqrt{17}$ sq. units
Area of triangle $= \frac{1}{2} | (\to A \times \to B) |$
$= \frac{1}{2} | (3^i - 6^j + 2^k) \times (2^i +^j - 2^k) |$
$= \frac{1}{2} \times | 10^i + 10^j + 15^k |$
$= \frac{5}{2} \times (\sqrt{17})$ sq. units

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Similar questions

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The vectors from the origin O to the points A and B is→A=3^i−6^j+2^k and →B=2^i+^j−2^k respectively. The area of triangle OAB be

The correct option is A 52√17 sq. unitsArea of triangle =12|(→A×→B)| =12|(3^i−6^j+2^k)×(2^i+^j−2^k)| =12×|10^i+10^j+15^k| =52×(√17) sq. units

The vectors from the origin $O$ to the points $A$ and $B$ is $\to A = 3^i - 6^j + 2^k$ and $\to B = 2^i +^j - 2^k$ respectively. The area of triangle $O A B$ be

The correct option is A $\frac{5}{2} \sqrt{17}$ sq. units
Area of triangle $= \frac{1}{2} | (\to A \times \to B) |$
$= \frac{1}{2} | (3^i - 6^j + 2^k) \times (2^i +^j - 2^k) |$
$= \frac{1}{2} \times | 10^i + 10^j + 15^k |$
$= \frac{5}{2} \times (\sqrt{17})$ sq. units