Advertisements
Advertisements
प्रश्न
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"`
Advertisements
उत्तर
Let `vec"a" = hat"i" + 2hat"j" + hat"k"` and `vec"b" = -hat"i" + 3hat"j" + 4hat"k"`.
Then `vec"a" xx vec"b" = |(hat"i", hat"j", hat"k"),(1, 2, 1),(-1, 3, 4)|`
= `hat"i"(8 - 3) - hat"j"(4 + 1) + hat"k"(3 + 2)`
= `5hat"i" - 5hat"j" + 5hat"k"`
⇒ `|vec"a" xx vec"b"| = sqrt((5)^2 + (-5)^2 + (5)^2)`
= `sqrt(3(5)^2)`
= `5sqrt(3)`
Therefore, unit vector perpendicular to the plane of `vec"a"` and `vec"b"` is given by
`(vec"a" xx vec"b")/|vec"a" xx vec"b"| = (5hat"i" - 5hat"j" + 5hat"k")/(5sqrt(3)`
Hence, vectors of magnitude of `10sqrt(3)` that are perpendicular to plane of `vec"a"` and `vec"b"` are `+-10sqrt(3) ((5hat"i" - 5hat"j" + 5hat"k")/(5sqrt(3)))`
i.e., `+- 10(hat"i" - hat"j" + hat"k")`.
APPEARS IN
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.
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`.
If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, find the angle which `veca + vecb + vecc`make with `veca or vecb or vecc`
Find the unit vector in the direction of \[3 \hat{i} + 4 \hat{j} - 12 \hat{k} .\]
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 \[\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} +\widehat{k} .\]
A vector \[\vec{r}\] is inclined at equal angles to the three axes. If the magnitude of \[\vec{r}\] is \[2\sqrt{3}\], find \[\vec{r}\].
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.
Find a vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} ,\] which has magnitude of 6 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
The magnitude of the vector `6hat"i" + 2hat"j" + 3hat"k"` is ______.
The vector in the direction of the vector `hat"i" - 2hat"j" + 2hat"k"` that has magnitude 9 is ______.
If the sum of two-unit vectors is a unit vector, then the magnitude of their difference 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`,
|
- What is the magnitude of the force of Team A ?
- Which team will win the game?
- Find the magnitude of the resultant force exerted by the teams.
OR
In what direction is the ring getting pulled?
