मराठी

The magnitude of the vector ijk6i^+2j^+3k^ is ______. - Mathematics

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प्रश्न

The magnitude of the vector `6hat"i" + 2hat"j" + 3hat"k"` is ______.

पर्याय

  • 5

  • 7

  • 12

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MCQ
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उत्तर

The magnitude of the vector `6hat"i" + 2hat"j" + 3hat"k"` is 7.

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Magnitude and Direction of a Vector
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पाठ 10: Vector Algebra - Solved Examples [पृष्ठ २११]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 10 Vector Algebra
Solved Examples | Q 10 | पृष्ठ २११

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Find the magnitude of the vector \[\vec{a} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k} .\]


Find the unit vector in the direction of \[3 \hat{i} + 4 \hat{j} - 12 \hat{k} .\]


If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is `sqrt(3)`.


If \[\vec{a} = \hat{i} + \hat{j} + \hat{k} , \vec{b} = 4 \hat{i} - 2 \hat{j} + 3 \hat{k} \text { and } \vec{c} = \hat{i} - 2 \hat{j} + \hat{k} ,\] find a vector of magnitude 6 units which is parallel to the vector \[2 \vec{a} - \vec{b} + 3 \vec{c .}\]


Find a vector of magnitude of 5 units parallel to the resultant of the vectors \[\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} +\widehat{k} .\]


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Write a vector of magnitude 12 units which makes 45° angle with X-axis, 60° angle with Y-axis and an obtuse angle with Z-axis.


Write the length (magnitude) of a vector whose projections on the coordinate axes are 12, 3 and 4 units.


Find a vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} ,\] which has magnitude of 6 units.


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Write a vector in the direction of vector \[5 \hat{i} - \hat{j} + 2 \hat{k}\] which has magnitude of 8 unit.


Find all vectors of magnitude `10sqrt(3)` that are perpendicular to the plane of `hat"i" + 2hat"j" + hat"k"` and `-hat"i" + 3hat"j" + 4hat"k"`


Prove that in a ∆ABC,  `sin"A"/"a" = sin"B"/"b" = sin"C"/"c"`, where a, b, c represent the magnitudes of the sides opposite to vertices A, B, C, respectively.


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Teams A, B, C went for playing a tug of war game. Teams A, B, C have attached a rope to a metal ring and is trying to pull the ring into their own area.

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Team B pulls with force F2 = `-4hati + 4hatj  kN`,

Team C pulls with force F3 = `-3hati - 3hatj  kN`,

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