हिंदी

Find the Magnitude of the Vector → a = 2 ^ I + 3 ^ J − 6 ^ K . - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Given: \[\vec{a} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k} .\]
∴ Magnitude of the vector = \[\left| \vec{a} \right| = \sqrt{2^2 + 3^2 + \left( - 6 \right)^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7\]

shaalaa.com
Magnitude and Direction of a Vector
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: Algebra of Vectors - Exercise 23.6 [पृष्ठ ४८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 23 Algebra of Vectors
Exercise 23.6 | Q 1 | पृष्ठ ४८

संबंधित प्रश्न

Find a vector `veca` of magnitude `5sqrt2` , making an angle of `π/4` with x-axis, `π/2` with y-axis and an acute angle θ with z-axis. 


Find `|veca| and |vecb|`, if `(veca + vecb).(veca -vecb) = 8 and |veca| = 8|vecb|.`


If `veca` is a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λ`veca` is unit vector if ______.


Find a vector of magnitude 5 units, and parallel to the resultant of the vectors `veca = 2i + 3hatj - hatk` and `vecb = hati - 2hatj + hatk`.


If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, show that the vector `veca +  vecb+ vecc` is equally inclined to `veca, vecb` and `vecc`.


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 \[\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} +\widehat{k} .\]


Find a vector \[\vec{r}\] of magnitude \[3\sqrt{2}\] units which makes an angle of \[\frac{\pi}{4}\] and \[\frac{\pi}{4}\] with y and z-axes respectively. 


Define "zero vector".


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.


Write two different vectors having same magnitude.


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


Find a vector in the direction of vector \[2 \hat{i} - 3 \hat{j} + 6 \hat{k}\] which has magnitude 21 units.


If in a ∆ABC, A = (0, 0), B = (3, 3 \[\sqrt{3}\]), C = (−3\[\sqrt{3}\], 3), then the vector of magnitude 2 \[\sqrt{2}\] units directed along AO, where O is the circumcentre of ∆ABC is 

 


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.


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


A vector `vec"r"` is inclined at equal angles to the three axes. If the magnitude of `vec"r"` is `2sqrt(3)` units, find `vec"r"`.


Find a vector of magnitude 6, which is perpendicular to both the vectors `2hat"i" - hat"j" + 2hat"k"` and `4hat"i" - hat"j" + 3hat"k"`.


Prove that in any triangle ABC, cos A = `("b"^2 + "c"^2 - "a"^2)/(2"bc")`, where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively.


Let `vecalpha = hati + 2hatj - hatk, vecbeta = 2hati - hatj + 3hatk, vecγ = 2hati + hatj + 6hatk`. If `vecalpha` and `vecbeta` are both perpendicular to a vector `vecδ` and `vecδ. vecγ` = 10, then the magnitude of `vecδ` is


Two equal forces acting at a point with an angle of 60° between them, if the resultant is equal `30sqrt(3)N`, the magnitude of the force will be


The area under a velocity-time curve represents the change in ______?


Which of the following statements is false about forces/ couple?


In a triangle ABC three forces of magnitudes `3vec(AB), 2vec(AC)` and `6vec(CB)` are acting along the sides AB, AC and CB respectively. If the resultant meets AC at D, then the ratio DC : AD will be equal to :


Read the following passage and answer the questions given below:

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.

Team A pulls with force F1 = `6hati + 0hatj  kN`,

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

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

  1. What is the magnitude of the force of Team A ?
  2. Which team will win the game?
  3. Find the magnitude of the resultant force exerted by the teams.
    OR
    In what direction is the ring getting pulled?

Find a vector of magnitude 20 units parallel to the vector `2hati + 5hatj + 4hatk`.


Find a vector of magnitude 9 units and perpendicular to the vectors.

`veca = 4hati - hatj + hatk` and `vecb = -2hati + hatj - 2hatk`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×