If 2 i -5 j and 3 i -4 j are 2 vectors in xy plane then the determinant - 2 5- 3 4 - will give the area of the formed by the two vectors in the x-y plane-A- parallelogramB- rhombusC- square

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Definition of a Determinant

If 2 i +5 j a...

Question

If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in xy plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the formed by the two vectors in the x-y plane.

parallelogram

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rhombus

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square

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Solution

The correct option is A parallelogram
We have discussed that the 2 vectors in x-y plane can be represented in the form of a matrix. For these two vectors the matrix will be $[\begin{matrix} 2 & 3 3 & 4 \end{matrix}]$ and the determinant of this gives the area of the parallelogram formed by them.

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If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in $x - y$ plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the parallelogram formed by the two vectors in the $x - y$ plane.

Q. The triangle formed by the three points whose position vectors are

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

and

3 i + 6 j - 3 k

, is

Q. The plane which can be formed with the vectors

¯ ¯ ¯ a = 3 ¯ i - 4 ¯ j + 2 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i - ¯ j - 6 ¯ ¯ ¯ k

¯ ¯ c = 5 ¯ i - 5 ¯ j - 4 ¯ ¯ ¯ k

Q. Is the triangle formed by the vectors

3 i + 5 j + 2 k, 2 i - 3 j - 5 k a n d - 5 i - 2 j + 3 k

equilateral?

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If 2i+5j and 3i+4j are 2 vectors in xy plane then the determinant ∣∣∣2534∣∣∣ will give the area of the formed by the two vectors in the x-y plane.

The correct option is A parallelogramWe have discussed that the 2 vectors in x-y plane can be represented in the form of a matrix. For these two vectors the matrix will be[2334]and the determinant of this gives the area of the parallelogram formed by them.

If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in xy plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the formed by the two vectors in the x-y plane.

The correct option is A parallelogram
We have discussed that the 2 vectors in x-y plane can be represented in the form of a matrix. For these two vectors the matrix will be $[\begin{matrix} 2 & 3 3 & 4 \end{matrix}]$ and the determinant of this gives the area of the parallelogram formed by them.