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AP EAMCET Engineering 23 Sep 2020 Shift 1 Paper

Section: Mathematics

Question : 5 of 160

Marks: +1, -0

Let

u

v

|u-v|=||u|-|v||

if and only if

Solution:

Concept:

The equality

|u-v| = ||u|-|v||

is the equality condition in the reverse triangle inequality.

Formula:

|u-v| \ge ||u|-|v||

Equality holds when

u

and

v

have the same direction.

Solution:

v = \lambda u

with

\lambda \ge 0

, then

|u-v| = |1-\lambda||u|

Also

||u|-|v|| = ||u|-\lambda|u|| = |1-\lambda||u|

Thus the given equality holds if and only if

u

and

v

are in the same direction.

Answer:

Option C:

u

and

v

have the same direction.

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