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The moment of the force, vec(F) = 4hat(i...

The moment of the force, `vec(F) = 4hat(i) + 5 hat(j) - 6 hat(k)` at (2, 0, -3), about the point (2, -2, -2), is given by

A

`-7hat(i) - 8hat(j) - 4hat(k)`

B

`-4hat(i) - hat(j) - 8hat(k)`

C

`-8hat(i) - 4hat(j) - 7hat(k)`

D

`-7hat(i) - 4hat(j) - 8hat(k)`

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In each of the following show that the given vectors are coplanar: vec(a) = hat (i) + hat (j) - 6 hat (k) , vec(b) = hat (i) + 3 hat (j) + 4 hat (k) , vec(c) = 2 hat (i) + 5 hat (j) + 3 hat (k)

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)

If vec (a) = 2 hat (i) - 3 hat (j) + 4 hat (k) and vec(b) = - 6 hat (i) + 9 hat (j) - 12 hat (k) , then

Find a unit vector perpendicular to both the vector vec(a) = 2 hat(i) + hat(j) - 2 hat(k) and vec(b) = 3 hat (i) - hat (j) + hat (k)

The scalar projection of vec(a) = 2 hat (i) - 3hat(j) + hat (k) on vec (b) = 3 hat(i) - 6 hat (j) - 2 hat (k)

Find the moment of vec F about point (2, -1, 3), where force vec F=3 hat i+2 hat j-4 hat k is acting on point (1, -1, 2).

Find the value of lamda if three vectors vec(a) = 2hat(i) - hat(j) + hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c) = 3hat(i) + lamda hat(j) + 5hat(k) are coplanar

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 )

If vec(alpha ) = hat (i) - 2 hat (j) + 3 hat (k) , vec(beta) = 2 hat (i) - 3 hat (j) + hat(k) and vec(gamma) = 3 hat (i) + hat (j) - 2 hat (k) , find vec(alpha) . (vec(beta)xx vec (gamma)) .

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

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