Home
Class 12
MATHS
f vec(a) is any vector , then -...

f `vec(a)` is any vector , then -

A

` (vec(a).hat(i))hat(i)+(vec(a).hat(j)) hat(j) + (veca.hat(k))hat(k) = vec(a)`

B

` (vec(a).hat(i))^(2)+(vec(a).hat(j)) ^(2)+ (vec(a) . hat(k))^(2)= |vec(a)|^(2)`

C

` hat (i)xx (vec(a)xx hat(j)) + hat(j)xx (vec(a) xx hat(j))+ hat(k) xx (vec(a)xxvec(k)) = 2 vec(a)`

D

all of the above

Text Solution

Verified by Experts

The correct Answer is:
A,B,C,D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integar Answer Type )|5 Videos

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Matrix Match Type )|2 Videos

  • PRODUCTS OF TWO VECTORS

    CHHAYA PUBLICATION|Exercise Exercise 2B ( Short answer type questions)|20 Videos

  • PROBABILITY

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|18 Videos

  • PROPERTIES OF TRIANGLE

    CHHAYA PUBLICATION|Exercise Assertion- Reason Type:|2 Videos

Similar Questions

Explore conceptually related problems

vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors and vec r is any vector in space, then ( veca × vecb )×( vecr × vecc )+( vecb × vecc )×( vecr × veca )+( vecc × veca )×( vecr × vecb ) is equal to

If vec(p) is a unit vector and ( vec (x) - vec(p)). (vec(x)+vec(p)) = 8 , then find |vec (x)|

Knowledge Check

  • If vec(a), vec(b),vec(c ) are any vectors, then which the following is equal to vec(a) xx vec(b) +vec(b)xx vec(c ) + vec(c ) xx vec(a) ?

    A
    `(vec(a)-vec(b))xx(vec(b)-vec(c))`
    B
    `(vec(c ) - vec(b)) xx (vec(a)- vec(c ))`
    C
    `(vec(a) - vec(b))xx (vec(a) - vec(c ))`
    D
    `1/2 { vec(a) xx(vec(b)-vec(c))+vec(b)xx(vec(c)-vec(a)) + vec(c )xx (vec(a)- vec(b))} `

  • Let vec(a), vec(b) and vec(c) be three non-zero vectors such that no two of them are collinear and (vec(a) xx vec(b)) xx vec(c) = (1)/(3) |vec(b)||vec(c)| vec(a) . If theta is the angle between vector vec(b) and vec(c) , then a value of sin theta is

    A
    `(2)/(3)`
    B
    `(-2sqrt3)/(3)`
    C
    `(2sqrt2)/(3)`
    D
    `(-sqrt2)/(3)`

    • Similar Questions

    Explore conceptually related problems

    Let the vectors vec a and vec b be such that | vec a|=3 and | vec b|=(sqrt(2))/3, then ,vec axx vec b is a unit vector, if the angel between vec a and vec b is?

    If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

    Define the position vector of a point with respect to an origin. If vec(a) " and " vec(b) are the position vectors of the points P and Q respectively, find the vector vec(PQ) in terms of vec(a) " and " vec(b) .

    If |veca+vecb|= |veca-vecb| ,(where veca and vec b are any vector) then show that veca and vecb are perpendicular to each other.

    If the vector product of a constant vector vec O A with a variable vector vec O B in a fixed plane O A B be a constant vector, then the locus of B is a. a straight line perpendicular to vec O A b. a circle with centre O and radius equal to | vec O A| c. a straight line parallel to vec O A d. none of these

    If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then find |vec x|

    Home
    Profile