Area of rhombus is - where diagonals are a- -2- -3- -5k- and b- - - -k-

The correct option is C √( 28.5 ) Given diagonals of a rhombus are a⃗ =2î 3ĵ +5k̂ and b⃗ = î +ĵ +k̂ Area of rhombus = 1 2 | a⃗×b⃗ #160; ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Area of rhomb...

Question

Area of rhombus is ______ , where diagonals are $\to a = 2^i - 3^j + 5^k$ and $\to b = -^i +^j +^k$

\sqrt{21.5}

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\sqrt{31.5}

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\sqrt{28.5}

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\sqrt{38.5}

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Solution

The correct option is C $\sqrt{28.5}$
Given diagonals of a rhombus are
$\to a = 2^i - 3^j + 5^k$ and $\to b = -^i +^j +^k$
Area of rhombus $= \frac{1}{2} ∣ ∣ \to a \times \to b ∣ ∣$
$= \frac{1}{2} ∣ ∣ (2^i - 3^j + 5^k) \times (-^i +^j +^k) ∣ ∣$
$= \frac{1}{2} ∣ ∣ - 8^i - 7^j -^k ∣ ∣ = \frac{1}{2} \sqrt{114}$
$= \sqrt{28.5}$

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Similar questions

Q. The three vectors

\to A = 3^i - 2^j +^k, \to B =^i - 3^j + 5^k

and

\to C = 2^i -^j + 4^k

form

Show that area of the prallelogram whose diagonals are given by $\to a a n d \to b i s \frac{\to a \times \to b}{2}$ . Also, find the area of the parallelogram, whose diagonals are $2^i -^j + k a n d^i + 3^j -^k .$

Q. Find the vector

\to r

which is perpendicular to

\to a =^i - 2^j + 5^k

and

\to b = 2^i + 3^j -^k

and

\to r . (2^i +^j +^k) + 8 = 0

Q. If

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

and

\to c = - 2^i +^j - 3^k

such that

\to r = l \to a + m \to b + n \to c

, then

Q. If

\to a = 2^i + 3^j +^k

\to b =^i -^j +^k

\to c =^i +^j +^k

and let

\to d

be such that

\to a \times \to b = \to d \times \to b, \to d \cdot \to c = 8

, then the value of

\to d . \to b

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Area of rhombus is ______ , where diagonals are →a=2^i−3^j+5^k and →b=−^i+^j+^k

The correct option is C √28.5Given diagonals of a rhombus are→a=2^i−3^j+5^k and →b=−^i+^j+^kArea of rhombus =12∣∣→a×→b∣∣ =12∣∣(2^i−3^j+5^k)×(−^i+^j+^k)∣∣ =12∣∣−8^i−7^j−^k∣∣=12√114 =√28.5

Area of rhombus is ______ , where diagonals are $\to a = 2^i - 3^j + 5^k$ and $\to b = -^i +^j +^k$