Let `a=hat(j)-hat(k) and b=hat(i)-hat(j)-hat(k)`. Then, the vector v satisfying `atimesb+c=0 and a*b=3`, is

Let vec a= hat j- hat k and vec c= hat i- hat j- hat k . Then vector vec b satisfying vec axx vec b+ vec c= vec0 and vec adot vec b=3 is (1) 2 vec i- vec j+2 vec k (2) hat i- hat j-2 hat k (3) hat i+j-2 hat k (4) - hat i+ hat j-2 hat k

Let a=alphahat(i)+2hat(j)-3hat(k), b=hat(i)+2alphahat(j)-2hat(k) and c=2hat(i)-alphahat(j)+hat(k) . Then the value of 6alpha , such that {(atimesb)times(btimesc)}times(ctimesa)=a , is

Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+hat(k) and d=hat(i)+hat(j)-hat(k) . Then, the line of intersection of planes one determined by a, b and other determined by c, d is perpendicular to

A, B and C are three vectors given by 2hat(i)+hat(k), hat(i)+hat(j)+hat(k) and 4hat(i)-3hat(j)+7hat(k) . Then, find R, which satisfies the relation RtimesB=CtimesB and R*A=0 .

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

A vector equally inclined to the vectors hat(i)-hat(j)+hat(k) and hat(i)+hat(j)-hat(k) then the plane containing them is

If a=2hat(i)+3hat(j)-hat(k), b=-hat(i)+2hat(j)-4hat(k), c=hat(i)+hat(j)+hat(k) , then find the value of (atimesb)*(atimesc) .

A vector(d) is equally inclined to three vectors a=hat(i)-hat(j)+hat(k), b=2hat(i)+hat(j) and c=3hat(j)-2hat(k) . Let x, y, z be three vectors in the plane a, b:b, c:c, a respectively, then