The two adjacent sides of a parallelogra...

The two adjacent sides of a parallelogram are `2 hat i - 4 hat j + 5 hat k` and `hat i - 2 hat j - 3 hat k`.Find the unit vector parallel to its diagonal.Also, find its area.

Text Solution

Verified by Experts

The correct Answer is:

`(1)/(7)(3hati-6hatj+2hatk);11sqrt(5)`

Topper's Solved these Questions

VECTOR ALGEBRA
NCERT TAMIL|Exercise EXERCISE 10.4|12 Videos
TWO DIMENSIONAL ANALYTICAL GEOMETRY-II
NCERT TAMIL|Exercise EXERCISE 5.6|25 Videos

Similar Questions

Explore conceptually related problems

The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 hat j+3 hat k . The unit vector parallel to one of the diagonals is a. 1/7(3 hat i+6 hat j-2 hat k) b. 1/7(3 hat i-6 hat j-2 hat k) c. 1/(sqrt(69))( hat i+6 hat j+8 hat k) d. 1/(sqrt(69))(- hat i-2 hat j+8 hat k)

Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat i - 2 hat j + hat k .

The adjacent sides of a parallelogram are vec a = 3 hat i + lambda hat j + 4 hat k and vec b = hat i - lambda hat j + hat k (i) Find vec a xx vec b (ii) If the area of the paralleogram is sqrt 42 square units, find the value of lambda .

If 3 hat i + 6 hat j + 2 hat k , hat i - 2 hat j + 3 hat k and 5 hat i + 2 hat j + m hat k are coplanar.

Find |vec a xx vec b| if vec a = 2 hat i - hat j + 3 hat k and vec b = 3 hat i - 5 hat j + 2 hat k .

Find the area of a parallelogram for which the vectors 2 hat i + hat j and 3 hat i + hat j + 4 hatk are adjacent sides.

For given vectors vec a = 2 hat i - hat j + 2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

If vec a.hat i= vec a.( hat i+ hat j)= vec a.( hat i+ hat j+ hat k) , then find the unit vector vec a

The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is

Find the area of a parallelogram whose adjacent sides are vec a = hat i + 2 hat j + 3 hat k and vec b = - 3 hat i - 2 hat j + hat k .

NCERT TAMIL-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10

Write down a unit vector in XY - plane making an angle of 30^(@) with ...
Text Solution
|
Find the scalar components and magnitude of the vector joining the poi...
Text Solution
|
A girl walks 4 km towards west, then she walks 3 km in a direction 30^...
Text Solution
|
If veca = vec b+ vec c, then is it true that |veca| = |vec b| + |vec ...
Text Solution
|
Find the value of x for which x (hat i + hat j + hat k) is a unit vect...
Text Solution
|
Find a vector of magnitude 5 units and parallel to the resultant of th...
Text Solution
|
If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatkandvecc=hati-2hatj+hatk, ...
Text Solution
|
Show that the points A(1, -2, -8) B (5, 0, -2) and C(11, 3, 7) are col...
Text Solution
|
Find the position vector of a point R which divides the line joining t...
Text Solution
|
The two adjacent sides of a parallelogram are 2 hat i - 4 hat j + 5 ha...
Text Solution
|
Show that the direction cosines of a vector equally inclined to the ax...
Text Solution
|
Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...
Text Solution
|
Thescalar product of the vector hat i + hat j + hat k with a unit vect...
Text Solution
|
If veca,vecb,vecc are mutually perpendicular vectors of equal magnitu...
Text Solution
|
Prove that (veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2), if and only...
Text Solution
|
If theta is the angle between two vectors vecaandvecb then veca*vecbge...
Text Solution
|
Let vecaandvecb be two unit vectors and theta is the angle between the...
Text Solution
|
The value of hati.(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjxxhati) ...
Text Solution
|
If theta is the angle between any two vectors vec a and vec b , then |...
Text Solution
|