If vec(a)=3hat(i)+hat(j)-4hat(k), vec(b)=6hat(i)+5hat(j)-2hat(k)and |vec(c )|=3, find the vector...

If vec(a)=(2hat(i)-hat(j)+hat(k)), vec(b)=(hat(i)-3hat(j)-5hat(k)) and vec(c)=(3hat(i)-4hat(j)-hat(k)) , find [vec(a)vec(b)vec(c)] and interpret the result.

If vec(a)=2hat(i)+3hat(j)+hat(k), vec(b)=hat(i)-2hat(j)+hat(k) and vec(c )=-3hat(i)+hat(j)+2hat(k) , find [vec(a)vec(b)vec(c )] .

verify that vec(a) xx (vec(b)+ vec(c))=(vec(a) xx vec(b))+(vec(a) xx vec(c)) , "when" (i) vec(a)= hat(i)- hat(j)-3 hat(k), vec(b)= 4 hat(i)-3 hat(j) + hat(k) and vec(c)= 2 hat(i) - hat(j) + 2 hat(k) (ii) vec(a)= 4 hat(i)-hat(j)+hat(k), vec(b)= hat(i)+hat(j)+ hat(k) and vec(c)= hat(i)- hat(j)+hat(k).

Find the value of lambda for which the vectors vec(a), vec(b), vec(c) are coplanar, where (i) vec(a)=(2hat(i)-hat(j)+hat(k)), vec(b) = (hat(i)+2hat(j)+3hat(k) ) and vec(c)=(3 hat(i)+lambda hat(j) + 5 hat (k)) (ii) vec(a)lambda hat(i)-10 hat(j)-5k^(2), vec(b) =-7hat(i)-5hat(j) and vec(c)= hat(i)--4hat(j)-3hat(k) (iii) vec(a)=hat(i)-hat(j)+hat(k), vec(b)= 2hat( i) + hat(j)-hat(k) and vec(c)= lambda hat(i) - hat(j) + lambda hat(k)

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

If vec(a)=2hat(i)-hat(j)+2hat(k) and vec(b)=6hat(i)+2hat(j)+3hat(k) , find a unit vector parallel to vec(a)+vec(b) .

If vec(a)=5hat(i)-hat(j)-3hat(k) and vec(b)=hat(i)+3hat(j)-5hat(k) , then show that the vectors (vec(a)+vec(b)) and (vec(a)-vec(b)) are perpendicular.

Find [vec(a)vec(b)vec(c)] , when (i) vec(a)=2hat(i)+hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=3hat(i)+hat(j)+2hat(k) (ii) vec(a)=2hat(i)-3hat(j)+4hat(k), vec(b)=hat(i)+2hat(j)-hat(k) and vec(c)=3hat(i)-hat(j)+2hat(k) (iii) vec(a) = 2 hat(i)-3hat(j), vec(b)=hat(i)+hat(j)-hat(k) and vec(c)=3hat(i)-hat(k)

Find vec(a).(vec(b)xx vec(c )) if : vec(a)=2hat(i)+hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c )=3hat(i)+hat(j)+2hat(k) .

If vec(a)=7hat(i)-2hat(j)+3hat(k), vec(b)=hat(i)-hat(j)+2hat(k), vec(c )=2hat(i)+8hat(j) , then find vec(a).(vec(b)xx vec(c )) and (vec(b)xx vec(c )).vec(a) .