Home
Class 11
MATHS
Let vecA, vecB and vecC be unit vectors ...

Let `vecA, vecB and vecC` be unit vectors such that `vecA.vecB = vecA.vecC=0` and the angle between `vecB and vecC " be" pi//3`. Then `vecA = +- 2(vecB xx vecC) `.

Text Solution

Verified by Experts

The correct Answer is:
1
`vecA, vecB and vecC` are three unit vectors such that
`vecA. vecB = vecA. vecC=0`
and the angle between `vecB and vecC " is " pi//3`
Now Eq, (i) show that `vecA` is perpendicular to both `vecB and vecC`. Thus
` vecB xx vecC = lambda vecA` . where `lambda` is any scalar.
`or |vecB xx vecC|=|lamda vecA|`
` or sin pi//3 = +- lambda`
( as `pi//3` is the angle between ` vecB and vecC`)
`or lambda = +- sqrt3//2`
` Rightarrow vecB xx vecC = +- sqrt3/2 vecA`
` or vecA =+- 2/sqrt3 (vecB xx vecC)`
There, the given statement is false.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.2|15 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise fill in the blanks|14 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos

Similar Questions

Explore conceptually related problems

Let vea, vecb and vecc be unit vectors such that veca.vecb=0 = veca.vecc . It the angle between vecb and vecc is pi/6 then find veca .

If veca, vecb, vecc are unit vectors such that veca. vecb =0 = veca.vecc and the angle between vecb and vecc is pi/3 , then find the value of |veca xx vecb -veca xx vecc|

Let veca, vecb, vecc be three unit vectors such that veca. vecb=veca.vecc=0 , If the angle between vecb and vecc is (pi)/3 then the volume of the parallelopiped whose three coterminous edges are veca, vecb, vecc is

Let veca, vecb, vecc be three unit vectors and veca.vecb=veca.vecc=0 . If the angle between vecb and vecc is pi/3 then find the value of |[veca vecb vecc]|

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then:

If veca,vecb,vecc,vecd are unit vectors such that veca.vecb=1/2 , vecc.vecd=1/2 and angle between veca xx vecb and vecc xx vecd is pi/6 then the value of |[veca \ vecb \ vecd]vecc-[veca \ vecb \ vecc]vecd|=

Let veca be a unit vector perpendicular to unit vectors vecb and vecc and if the angle between vecb and vecc " is " alpha , " then " vecb xx vecc is

Let veca =2hati +hatj -2hatk and vecb = hati +hatj . " Let " vecc be vector such that |vecc -veca|=3, |(veca xx vecb) xx vecc|=3 and the angle between vecc and veca xx vecb " be " 30^(@) Then , veca . Vecc is equal to

If veca, vecb,vecc are unit vectors such that veca is perpendicular to the plane of vecb, vecc and the angle between vecb,vecc is pi/3 , then |veca+vecb+vecc|=

If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0 , then the value of veca.vecb+vecb.vecc+vecc.veca is