मराठी

Find the direction cosines of the vector i^+2j^+3k^.

Advertisements
Advertisements

प्रश्न

Find the direction cosines of the vector `hati + 2hatj + 3hatk`.

बेरीज
Advertisements

उत्तर

Let `veca = hati + 2hatj + 3hatk`

`therefore |veca| = sqrt(1^2 + 2^2 + 3^2) `

`= sqrt(1 + 4 + 9)`

`= sqrt14`

Hence, the direction cosines of `veca` are `(1/sqrt14, 2/sqrt14, 3/sqrt14)`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 10: Vector Algebra - Exercise 10.2 [पृष्ठ ४४०]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 10 Vector Algebra
Exercise 10.2 | Q 12. | पृष्ठ ४४०

संबंधित प्रश्‍न

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are -2, 1, -1, and -3, -4, 1.


If `bara, barb, bar c` are the position vectors of the points A, B, C respectively and ` 2bara + 3barb - 5barc = 0` , then find the ratio in which the point C divides line segment  AB.


Write the position vector of the point which divides the join of points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.


Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector

`2hati+3hatj+4hatk` to the plane `vecr` . `(2hati+hatj+3hatk)−26=0` . Also find image of P in the plane.


Classify the following measures as scalar and vector.

10 kg


Classify the following as scalar and vector quantity.

Time period


Two collinear vectors are always equal in magnitude.


Two vectors having the same magnitude are collinear.


Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  `hati + 2hatj - hatk` and `-hati + hatj + hatk`  respectively, externally in the ratio 2:1.


Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis.


Express \[\vec{AB}\]  in terms of unit vectors \[\hat{i}\] and \[\hat{j}\], when the points are A (4, −1), B (1, 3)
Find \[\left| \vec{A} B \right|\] in each case.


Express \[\vec{AB}\]  in terms of unit vectors \[\hat{i}\] and \[\hat{j}\], when the points are A (−6, 3), B (−2, −5)
Find \[\left| \vec{A} B \right|\] in each case.


Dot product of a vector with \[\hat{i} + \hat{j} - 3\hat{k} , \hat{i} + 3\hat{j} - 2 \hat{k} \text{ and } 2 \hat{i} + \hat{j} + 4 \hat{k}\] are 0, 5 and 8 respectively. Find the vector.


The adjacent sides of a parallelogram are represented by the vectors \[\vec{a} = \hat{i} + \hat{j} - \hat{k}\text{ and }\vec{b} = - 2 \hat{i} + \hat{j} + 2 \hat{k} .\]
Find unit vectors parallel to the diagonals of the parallelogram.


Show that the vectors \[\vec{a} = \frac{1}{7}\left( 2 \hat{i} + 3 \hat{j} + 6 \hat{k} \right), \vec{b} = \frac{1}{7}\left( 3\hat{i} - 6 {j} + 2 \hat{k} \right), \vec{c} = \frac{1}{7}\left( 6 \hat{i} + 2 \hat{j} - 3 {k} \right)\] are mutually perpendicular unit vectors. 


For any two vectors \[\vec{a} \text{ and } \vec{b}\] show that \[\left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) = 0 \Leftrightarrow \left| \vec{a} \right| = \left| \vec{b} \right|\]


If \[\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}\]  \[\vec{b} = \hat{i} + \hat{j} - 2 \hat{k}\]  \[\vec{c} = \hat{i} + 3 \hat{j} - \hat{k}\] find λ such that \[\vec{a}\] is perpendicular to \[\lambda \vec{b} + \vec{c}\]  


If either \[\vec{a} = \vec{0} \text{ or } \vec{b} = \vec{0}\]  then \[\vec{a} \cdot \vec{b} = 0 .\] But the converse need not be true. Justify your answer with an example. 


Show that the vectors \[\vec{a} = 3 \hat{i} - 2 \hat{j} + \hat{k} , \vec{b} = \hat{i} - 3 \hat{j} + 5 \hat{k} , \vec{c} = 2 \hat{i} + \hat{j} - 4 \hat{k}\] form a right-angled triangle. 


Find the angles of a triangle whose vertices are A (0, −1, −2), B (3, 1, 4) and C (5, 7, 1). 


If \[\overrightarrow{AO} + \overrightarrow{OB} = \overrightarrow{BO} + \overrightarrow{OC} ,\] prove that A, B, C are collinear points.


If `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.


Find the sine of the angle between the vectors `vec"a" = 3hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" - 2hat"j" + 4hat"k"`.


The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as


Let (h, k) be a fixed point where h > 0, k > 0. A straight line passing through this point cuts the positive direction of the coordinate axes at the points P and Q. Then the minimum area of the ΔOPQ. O being the origin, is


Area of rectangle having vertices A, B, C and D will position vector `(- hati + 1/2hatj + 4hatk), (hati + 1/2hatj + 4hatk) (hati - 1/2hatj + 4hatk)` and `(-hati - 1/2hatj + 4hatk)` is


Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6x − 12 = 3y + 9 = 2z − 2


Which physical quantity has magnitude only?


Which physical quantity has magnitude as well as direction?


In the vector \[\vec{AB}\], what are A and B respectively?


What does \[\vec{AB}\] represent?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×