If - and b- are two unit vectors- then the vector - - b- - -b- is parallel to

The correct option is C ( â #160; b̂) Given #160; â,b̂ are unit vector â=î b̂=ĵ (â+b̂)×(â×b̂) =(î+ĵ)×(î×ĵ) =(î+ĵ)×(k̂) ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If â and ...

Question

If $^a$ and $^b$ are two unit vectors, then the vector $(^a +^b) \times$ $(^a \times^b)$ is parallel to

(^a -^b)

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(^a +^b)

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(2^a -^b)

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(2^a +^b)

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Solution

The correct option is C $(^a -^b)$
Given
$^a,^b$ are unit vector
$^a =^i$
$^b =^j$

$(^a +^b) \times (^a \times^b)$
$= (^i +^j) \times (^i \times^j)$
$= (^i +^j) \times (^k)$
$=^i \times^k +^j \times^k$
$= -^j +^i$
$=^a -^b$
If we cross product with $(^a -^b)$
$(^a -^b) \times (^a -^b)$
$= 0$
Hence it is parallel to $^a -^b$ .

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If ^a and ^b are two unit vectors, then the vector (^a+^b)× (^a×^b) is parallel to

The correct option is C (^a−^b)Given ^a,^b are unit vector^a=^i^b=^j(^a+^b)×(^a×^b)=(^i+^j)×(^i×^j)=(^i+^j)×(^k)=^i×^k+^j×^k=−^j+^i=^a−^bIf we cross product with (^a−^b)(^a−^b)×(^a−^b)=0Hence it is parallel to ^a−^b.

If $^a$ and $^b$ are two unit vectors, then the vector $(^a +^b) \times$ $(^a \times^b)$ is parallel to