2hat(i)-2hat(j)-3hat(k) और4 hat(i) +3hat(j) -hat(k) का अदिश गुणनफल ज्ञात कीजिए | | 11 | संदिश वि...

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

The two vectors A=2hat(i)+hat(j)+3hat(k) and B=7hat(i)-5hat(j)-3hat(k) are :-

Find the shortest distance between the lines : vec(r) = (4hat(i) - hat(j)) + lambda(hat(i) + 2hat(j) - 3hat(k)) and vec(r) = (hat(i) - hat(j) + 2hat(k)) + mu (2hat(i) + 4hat(j) - 5hat(k))

Show that the vectors 2hat(i)-hat(j)+hat(k) and hat(i)-3hat(j)-5hat(k) are at right angles.

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)

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) .

If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

If a=hat(i)+2hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=hat(i)+3hat(j)-hat(k) , then atimes(btimesc) is equal to

If vector hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k) and 2hat(i)+3hat(j)+lambda hat(k) are coplanar, then lambda is equal to