The position vectors of the points A and...

The position vectors of the points A and B are `vec i + 2 vec j + 3 vec k` and ` 2 vec i - vec j - vec k` respectively. Find the projection of `vec (AB)` on the vector `vec i + vec j + vec k`. Also find the resolved part of `vec (AB) ` in that direction.

Text Solution

AI Generated Solution

Topper's Solved these Questions

Product of two Vectors
A DAS GUPTA|Exercise Exercise|48 Videos
Product of three or more Vectors
A DAS GUPTA|Exercise Exercise|28 Videos
Progression, Related Inequalities and Series
A DAS GUPTA|Exercise Exercise|235 Videos

Similar Questions

Explore conceptually related problems

If the position vectors of two given points A and B be 8vec i+3vec j+2vec k and 2vec i-5vec j+3vec k respectively,find the magnitude and direction of vec AB

if vec b=2 vec i + 3 vec j - vec k and vec c= vec i + 4 vec j + 5 veck then find a vector vec a such that vec b * vec a =0 and vec c * vec a=0 . Also find the unit vector along vec a .

If vec a=hat i-hat j and vec b=-hat j+hat k find the projection of vec a on vec b

(vec i + xvec j + 3vec k) xx (vec i-vec j + vec k) = 5vec i + xvec j-3vec k then x =

The position vectors of the points A,B,C , D are respectively 2 vec i + vec j - vec k, vec i + vec j + vec k, vec i- 2 vec j+ 3 vec k and 3 vec i- vec j + 2 vec k . Evaluate [vec (AB), vec (AC), vec (AD)] .

The position vectors of three points are vec i+3vec j-2vec k,3vec i-2vec j+vec k and -2vec i+vec j+3vec k show that the points are the vertices of an equilateral triangle

Find the value of: (vec j xxvec k) * (3vec i + 2vec j-vec k)

The position vectors of three points are -2vec i+3vec j+5vec k,vec i+2vec j+3vec k,7vec i-vec k Show that the three points are collinear

The sine of the angle between the vectors vec i+3vec j+2vec k and 2vec i-4vec j+vec k is

vec a = vec i + 2vec j + 3vec k, vec b = -vec i + 2vec j + vec k, rArr3vec i + vec j and vec d is normal to both vec a and vec b then (vec c, vec d)

A DAS GUPTA-Product of two Vectors-Exercise

The position vectors of the points A and B are vec i + 2 vec j + 3 vec...
Text Solution
|
For any vector vec r , prove that vec r=( vec rdot hat i) hat i+( ve...
Text Solution
|
If |vec(a)+vec(b)||=|vec(a)-vec(b)| then show that vec(a) and vec(b) a...
Text Solution
|
Let hat(a), hat(b) be two unit vectors and theta be the angle between...
Text Solution
|
Prove that |vec a + vec b| = sqrt (|vec a|^2 + |vec b|^2 + 2 vec a * ...
Text Solution
|
Prove that , ( vec(a) xx vec(b))^(2) + (vec (a).vec(b))^(2) = |ve...
Text Solution
|
If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then show that veca...
Text Solution
|
Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b...
Text Solution
|
If |vec a|=1=|vec b| and |vec a + vec b|=sqrt3 then evaluate (2 vec a ...
Text Solution
|
Find lambda such that the scalar product of the vector vec i + vec j +...
Text Solution
|
The set of values of x for which the angle between the vectors vec a= ...
Text Solution
|
Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. ...
Text Solution
|
Vectors 3 vec a-5 vec ba n d2 vec a= vec b are mutually perpendicular....
Text Solution
|
The pth, qth and rth terms of a GP are the positive numbers a,b and c ...
Text Solution
|
If vec a, vec b , vec c are mutually perpendicular vectors of equal ma...
Text Solution
|
A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a...
Text Solution
|
vec a , vec b and vec c are the position vectors of points A ,B and C...
Text Solution
|
Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...
Text Solution
|
If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...
Text Solution
|
A , B , Ca n dD are any four points in the space, then prove that |...
Text Solution
|
If the angle between the vectors x vec i + vec j - vec k and vec i + x...
Text Solution
|