Prove that (veca+vecb) cdot (veca+vecb) ...

Prove that `(veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2`, if and only if `veca, vecb` are perpendicular, given `veca ne vec0, vecb ne vec0`.

Topper's Solved these Questions

VECTORS
MODERN PUBLICATION|Exercise Exercise|500 Videos
UNIT TEST-4
MODERN PUBLICATION|Exercise EXERCISE|13 Videos

Similar Questions

Explore conceptually related problems

Prove that |veca|-|vecb| le|veca - vecb | .

Prove that veca*((vecb+vecc)xx(veca+vecb+vecc))=0 .

Prove that : (vecaxxvecb)^2=|\veca|^2.|\vecb|^2-(veca.vecb)^2 .

If |veca+vecb|=|veca-vecb| then show that veca and vecb are perpendicular.

If veca*vecb=-|veca||vecb| , then theta=

Prove that {(vecb+vecc)xx(vecc+veca)}.(veca+vecb)=2[veca,vecb,vecc]

If veca*vecb=-|veca|*|vecb| , then theta= ,

If 2(veca.vecb)= |veca||vecb| then angle between veca and vecb equals to ,

MODERN PUBLICATION-VECTORS-Exercise

If |veca+vecb|=|veca-vecb| then show that veca and vecb are perpendicu...
Text Solution
|
If veca and vecb are perpendicular vectors, show that (veca+vecb)^(2)=...
Text Solution
|
Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2, if and ...
Text Solution
|
Three vectors veca, vecb, vecc satisfy the condition veca+vecb+vecc=v...
Text Solution
|
If the vectors veca,vecb and vecc satisfy the condition veca+vecb+vecc...
Text Solution
|
The scalar product of the vector veca=hati+hatj+hatk with a unit vecto...
Text Solution
|
If |veca|=3, |vecb|=4 and |vecc|=5 and each of them is perpendicular ...
Text Solution
|
If veca and vecb are perpendicular vectors, show that (veca+vecb)^(2)=...
Text Solution
|
IF veca=3hati+hatj-4hatk,vecb=6hati+5hatj-2hatk and |vecc|=3, find the...
Text Solution
|
If veca=hati+4hatj+2hatk , vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+...
Text Solution
|
Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+4...
Text Solution
|
Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+4...
Text Solution
|
If veca=hati-hatj, vecb= 3hatj-hatk and vecc=7hati-hatk. Find a vector...
Text Solution
|
Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the...
Text Solution
|
Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the...
Text Solution
|
Dot-product of a vector with vectors 3hati-5hatk,2hati+7hatj and hati+...
Text Solution
|
If hati+hatj+hatk, 2hati+5hatj, 3hati+2hatj-3hatk and hati-6hatj-hatk ...
Text Solution
|
If vecalpha=3hati+4hatj+5hatk and vecbeta=2hati+hatj-4hatk, then expre...
Text Solution
|
Prove that the perpendicular from the vertices to the opposite sides (...
Text Solution
|
Prove that in a right angled triangle the mid-point of the hypotenuse ...
Text Solution
|