Home
Class 12
MATHS
Let overset(to)(a) = hat(i) - hat(j) ,...

Let `overset(to)(a) = hat(i) - hat(j) , overset(to)(b) - hat(k) , overset(to)( c) - hat(k) - hat(i) .` If `overset(to)(d)` is a unit vector such that `overset(to)(a) , Overset(to)(d) =0= [ overset(to)(b) overset(to)(c ) overset(to)d)]` then `overset(to)(d)` equals

A

`+- . (hat(i)+hat(j)-2hat(k))/(sqrt(6))`

B

`+- . (hat(i) + hat(j) - hat(k))/(sqrt(3))`

C

` +- . (hat(i) + hat(j) + hat(k))/(sqrt(3))`

D

` +- hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `vec(d) = xhat(i) +yhat(j) +zhat(k)`
where `x^(2) + y^(2) + z^(2) =1`
Since `vec(a) ". " vec(d) =0`
` rArr x-y =0rArr x=y`
Also `[vec(b) vec(c ) vec(d)] =0`
`rArr |{:(0,,1,,-1),(-1,,0,,1),(x,,y,,z):}|=0 rArr x+y+ z=0`
`rArr 2x+ z=0 `
From Eqs (i) , (ii) and (iii)
`x^(2) +x^(2) +4x^(2) = 1 rArr x = +- (1)/(sqrt(6))`
`:. vec(d) = +- (1)/(sqrt(6)) (hat(i) +hat(j) - 2hat(k))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let overset(to)(a) =2hat(i) + hat(j) -2hat(k) " and " overset(to)(b) = hat(i) + hat(j) . " If " overset(to)(c ) is a vectors such that |overset(to)(a)"." overset(to)(c ) = |overset(to)( c)| , |overset(to)(c )- overset(to)(a)|= 2sqrt(2) and the angle between (overset(to)(a) xx overset(to)(b)) " and " overset(to)( c ) " is " 30^(@), " then "|(overset(to)(a) xx overset(to)(b)) xx overset(to)( c )| is equal to

The scalar overset(to)(A) .[(overset(to)(B) xx overset(to)( C)) xx (overset(to)(A) + overset(to)(B) + overset(to)( C))] equals

If overset(to)(a) , overset(to)(b) " and " overset(to)( c) are unit coplanar vectors then the scalar triple product [2 overset(to)(a) - overset(to)(b) 2 overset(to)(b) - overset(to)(c ) 2 overset(to)(c ) - overset(to)(a)] is

If overset(to)(a) , overset(to)(b) , overset(to)(c ) " and " overset(to)(d) are the unit vectors such that (overset(to)(a)xx overset(to)(b)). (overset(to)(c )xx overset(to)(d)) =1 " and " overset(to)(a), overset(to)(c ) = .(1)/(2) , then

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

If overset(to)(a) =hat(i) - hat(k) , overset(to)(b) = x hat(i) + hat(j) + (1-x) hat(k) and overset(c ) =y hat(i) +x hat(j) + (1+x-y) hat(k) . "Then " [overset(to)(a) , overset(to)(b) , overset(to)( c) ] depends on

If overset(to)(A) = 2hat(i) + hat(k) , overset(to)(B) = hat(i) + hat(j) +hat(k) " and " overset(to) (C ) = 4hat(i) - 3hat(j) +7hat(k) Determine a vector overset(to)(R ) " satisfying " overset(to)(R ) xx overset(to)( B) = overset(to)( C ) xx overset(to)( B) " and " overset(to)(R ) " ." overset(to)(A) = 0

If overset(to)(a) = (hat(i) + hat(j) + hat(k)) , overset(to)(a) , overset(to)(b) , overset(to)(c ) =1 " and " overset(to)(a) xx overset(to)(b) = hat(j) - hat(k), " then " overset(to)(b) is equal to

if overset(to)(a),overset(to)(b) " and " overset(to)(c ) are unit vectors then |overset(to)(a)-overset(to)(b)|^(2)+|overset(to)(b)-overset(to)c|^(2)+|overset(to)(c)-overset(to)(a)|^(2) does not exceed

Let overset(to)(a) =2hat(i) +hat(j) + hat(k), overset(to)(b) =hat(i) + 2hat(j) -hat(k) and a unit vector overset(to)(c ) be coplanar. If overset(to)(c ) is perpendicular to overset(to)(a) " then " overset(to)(c ) is equal to