Question

Question No. 16.
Area of the parallelogram formed by
vectors 31 – 2; + k and î + 25 + 3k is
38 Sq units
24
Sq units
83 Sq units
None​

Answer 1

Question :-

Area of the parallelogram formed by vectors 3i - 2j + k and i + 25j + 3k

Answer :-

Given :-

◉ Vector A = 3i - 2j + k

◉ Vector B = i + 25j + k

We need to find the area of Parallelogram formed by these vectors.

Let us find the cross product of vector A and vector B.

| i j k |

⇒ A × B = | 3 -2 1 |

| 1 25 1 |

⇒ A × B = (-2×1 - 25×1)i - (3×1 - 1×1)j + (25×3 - 1×-2)k

⇒ A × B = (-2 - 25)i - (3-1)j + (75+2)k

⇒ A × B = -27i - 2j + 77k

We know,The magnitude of vector formed by Cross product of two vectors is the area of the Parallelogram formed by that two vectors.

⇒ Area = √[(-27)² + (-2)² + (77)² ]

⇒ Area = √(729 + 4 + 5929)

⇒ Area = √6662

⇒ Area = 81.62 sq. units

None of the options matched with our answer.

∴ Option (D) - None

Answer 2

Option (c) 24sq units..