बिंदु `(a, b, c)` से जाने वाले तथा तल `overline(r). (hat(i) + hat(j) + hat(k)) = 2` के समांतर ताल का समीकरण ज्ञात कीजिए।

If overline(a)*hat(i)=4, then (overline(a)timeshat(j))*(2hat(j)-3hat(k))=

If angle bisector of overline(a) = 2hat(i) + 3 hat(j) + 4 hat(k) and overline(b) = 4hat(i) - 2 hat(j) + 3 hat(k) is overline(c ) = alpha hat(i) + 2 hat(j) + beta hat(k) then

If vec(a) = hat (i) + hat (j) - hat (k) , vec (b) = 2 hat (i) - 2 hat (j) + hat (k) and vec(c ) = 3 hat (i) + 2 hat (j) - 2 hat (k) show that , vec (a). (vec(b)+vec(c)) = vec (a).vec(b) + vec (a).vec(c )

(overline(a)*hat(i))hat(i)+(overline(a)*hat(j))hat(j)+(overline(a)*hat(k))hat(k))=

A plane is at a distance of 5 units from the origin and perpendicular to the vector 2hat(i) + hat(j) + 2hat(k) . The equation of the plane is a) vec(r ).(2hat(i) + hat(j) -2hat(k))=15 b) vec(r ).(2hat(i)+ hat(j)-hat(k))=15 c) vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15 d) vec(r ).(hat(i) + hat(j) + 2hat(k))=15

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab