Home
Class 12
MATHS
If vec(alpha) is a unit vector, vec(beta...

If `vec(alpha)` is a unit vector, `vec(beta)= hat(i) + hat(j) - hat(k), vec(gamma) = hat(i) + hat(k)`, then the maximum value of `[vec(alpha) vec(beta) vec(gamma)]` is

A

3

B

`sqrt""3`

C

2

D

`sqrt""6`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

Let vec(alpha)=hat(i) +2 hat(j) - hat(k), vec(beta) = 2 hat(i) - hat(j) + 3 hat(k) and vec(lambda)=2hat(i) + hat(j) + 6 hat(k) be three vectors. If vec(alpha) and vec(beta) are both perpendicular to the vector vec(delta) and vec(delta).vec(lambda)=10 , then what is the magnitude of vec(delta) ?

If vec(A) = hat(i) + hat(j) + hat(k) and B = -hat(i) - hat(j) - hat(k) . Then angle made by (vec(A) - vec(B)) with vec(A) is :

Let a vector vec(a) be coplanar with vectors vec(b) = 2hat(i) + hat(j) + hat(k) and vec(c) = hat(i) - hat(j) + hat(k) . If vec(a) is perpendicular to vec(d) = 3hat(i) + 2hat(j) + 6hat(k) , and |vec(a)| = sqrt(10) . Then a possible value of [[vec(a),vec(b),vec(c)]] + [[vec(a), vec(b), vec(d)]] + [[vec(a),vec(c),vec(d)]] is equal to :

If vectors vec(a)=hat(i)-2hat(j)+hat(k), vec(b)=-2hat(i)+4hat(j)+5hat(k) and vec(c )=hat(i)-6hat(j)-7hat(k) , then find the value of |vec(a)+vec(b)+vec(c )| .

If vec(a) = alpha hat(i) + beta hat(j)+ 3 hat(k) , vec(b) = - beta hat(i) - alpha hat(j) - hat(k) and vec( c ) = hat(i) - 2hat(j) - hat(k) such that vec( a) . vec(b) =1 and vec( b ).vec(c ) = - 3 then (1)/(3) ((vec(a) xx vec(b)).vec( c)) is equal to "________" .

If vec(a) = hat(i) + 2 hat(j) + 3 hat(k) and vec(b) = 2 hat(i) + 3 hat(j) + hat(k) , find a unit vector in the direction of ( 2 vec(a) + vec(b)) .