The work done in moving an object along the vector $\vec{d} = 3i + 2j - 5k$,if the applied force is $\vec{F} = 2i - j - k$,is

If $A, B, C, D$ are the points $(2, 3, -1), (3, 5, -3), (1, 2, 3), (3, 5, 7)$ respectively,then the angle between $AB$ and $CD$ is

The vector$(s)$ which is/are coplanar with vectors $\hat{i}+\hat{j}+2\hat{k}$ and $\hat{i}+2\hat{j}+\hat{k}$,and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are:
$(A) \hat{j}-\hat{k}$
$(B) -\hat{i}+\hat{j}$
$(C) \hat{i}-\hat{j}$
$(D) -\hat{j}+\hat{k}$

If three consecutive vertices of a parallelogram are $A(4,3,5)$,$B(0,6,0)$,$C(-8,1,4)$ and $D$ is the fourth vertex,then the angle between $AC$ and $BD$ is

If $a \times r = b + \lambda a$ and $a \cdot r = 3,$ where $a = 2i + j - k$ and $b = -i - 2j + k,$ then $r$ and $\lambda$ are equal to

If $|a \times b| = 4$ and $|a \cdot b| = 2$,then $|a|^2 |b|^2 = $