Home
Class 12
MATHS
Let us define the length of a vector aha...

Let us define the length of a vector `ahati+bhatj+chatk` and `|a|+|b|+|c|`. This definition coincides with the usual definition of length of a vector `ahati+bhatj+chatk` if an only if

A

a=b=c=0

B

any two of a,b and c are zero

C

any one of a,b and c is zero

D

a+b+c=0

Text Solution

Verified by Experts

The correct Answer is:
B
`|a|+|b|+|c|=sqrt(a^(2)+b^(2)+c^(2))`
`hArr 2|ab|+2|bc|+2|ca|=0`
`hArr ab=bc=ca=0 hArr` any two of a,b and c are zero.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the condition that the three points whose position vectors, a=ahati+bhatj+chatk,b=hati+chatj and c=-hati-hatj are collinear.

If the vectors ahati+hatj+hatk,hati+bhatj+hatk and hati+hatj+chatk are coplanar (a ne b ne c ne 1) , then the value of abc - (a+b+c) =

Read each statement below carefully and state with reasons , if it is true of false : (a) The magnitude of a vector is always a scalar , (b) each component of a vector is always a scalar , (c ) the total path length is always equal to the magnitude of the displacement vector of a particle . (d) the average speed of a either greater or equal to the magnitude of average velocity of the particle over the same interval of time , (e ) Three vectors not lying in a plane can never add up to give a null vector .

Let a,b and c be distinct non-negative numbers and the vectors ahati+ahatj+chatk,hati+hatk,chati+chatj+bhatk lie in a plane, then the quadratic equation ax^(2)+2cx+b=0 has

A unit vector is represented by ahati+bhatj+chatk If the values of 'a' and 'b' are 0.6 and 0.8 respectively, then find the value of 'c'.

If the position vectors of the points A,B and C be hati+hatj,hati-hatj and ahati+bhatj+chatk respectively, then the points A,B and C are collinear, if

The position vectors of the vertices A,B and C of a triangle are hati-hatj-3hatk,2hati+hatj-2hatk and -5hati+2hatj-6hatk , respectively. The length of the bisector AD of the angleBAC , where D is on the segment BC, is