Advertisements
Advertisements
प्रश्न
Find a vector in the direction of vector \[2 \hat{i} - 3 \hat{j} + 6 \hat{k}\] which has magnitude 21 units.
Advertisements
उत्तर
Let \[\overrightarrow{a} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k}\]
\[\therefore \left| \overrightarrow{a} \right| = \sqrt{2^2 + \left( - 3 \right)^2 + 6^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7\]
Unit vector in the direction of \[\overrightarrow{a} = \frac{\overrightarrow{a}}{\left| \overrightarrow{a} \right|} = \frac{2 \hat{i} - 3 \hat{j} + 6 \hat{k}}{7}\]
∴ Vector in the direction of vector \[\overrightarrow{a}\] which has magnitude 21 units
\[= 21 \times \left( \frac{2\hat{i} - 3 \hat{j} + 6 \hat{k}}{7} \right)\]
\[ = 3\left( 2 \hat{i} - 3 \hat{j} + 6 \hat{k} \right)\]
\[ = 6 \hat{i} - 9 \hat{j} + 18 \hat{k}\]
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 the magnitude of two vectors `veca and vecb`, having the same magnitude and such that the angle between them is 60° and their scalar product is `1/2`.
If `veca` is a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λ`veca` is unit vector if ______.
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`
Represent the following graphically:
(i) a displacement of 40 km, 30° east of north
(ii) a displacement of 50 km south-east
(iii) a displacement of 70 km, 40° north of west.
Find the magnitude of the vector \[\vec{a} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k} .\]
If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is `sqrt(3)`.
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.
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.
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 \[\overrightarrow{a}\] of magnitude \[5\sqrt{2}\], making an angle of \[\frac{\pi}{4}\] with x-axis, \[\frac{\pi}{2}\] with y-axis and an acute angle θ with z-axis.
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 ______.
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.
The vector in the direction of the vector `hat"i" - 2hat"j" + 2hat"k"` that has magnitude 9 is ______.
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 :
The magnitude of the vector `6hati - 2hatj + 3hatk` is ______.
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`
