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) ...

211

You visited us 211 times! Enjoying our articles? Unlock Full Access!

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)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(^a +^b)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(2^a -^b)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(2^a +^b)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $^a -^b$ .

Suggest Corrections

Similar questions

Q. Arrange the value of

| a + b + c |

in ascending order

A

.If

^a,^b,^c

are mutually perpendicular unit vectors

B

. If

^a,^b,^c

are vectors of lengths 2,3,4 respectively and

^a,^b,^c

are perpendicular to

^b +^c,^c +^a,^a +^b

respectively.

C

. If

^a,^b,^c

are vectors of lengths 4,4,5 respectively and

^a,^b,^c

are perpendicular to

^b +^c

^c +^a

^a +^b

respectively.

Q. If

^a

^b

and

^c

are unit vectors satisfying

|^a -^b |^{2} + |^b -^c |^{2} + |^c -^a |^{2} = 9

, then

| 2^a + 5^b + 5^c |

Q. If

^a

^b

are unit vectors such that

^a +^b

is also a unit vector then the angle between the vectors

^a

and

^b

Q. If three unit vector

^a,^b,^c

satisfy

^a +^b +^c =^0

, then the angle between

^a

and

^b

Q. Let

^a,^b,^c

be unit vectors and

α, β, γ

are angles between the vectors

^a,^b;^b,^c

and

^c,^a

respectively. If

^a +^b +^c

is also a unit vector then

cos α + cos β + cos γ

is equal to

Join BYJU'S Learning Program

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