The position vectors of the four angu...

The position vectors of the four angular points of a tetrahedron are `A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot` Find the volume of the tetrahedron `A B C Ddot`

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The four points whose position vector are 6 hat i - 7 hat j,16 hat i - 29 hat j - 4 hat k, 3 hat j - 6 hat k, 2 hat i + 5 hat j + 10 hat k are coplanar

Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k and 2 hat i + 5 hat j - hat k from a triangle in space.

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

Show that the four points having position vectors 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k ,2 hat i-5 hat j+10 hat k are coplanar.

Dot product of a vector with hat i+ hat j-3 hat k ,\ hat i+3 hat j-2 hat k\ a n d\ 2 hat i+ hat j+4 hat k are 0, 5 and 8 respectively. Find the vector.

Dot product of a vector with hat i+ hat j-3 hat k , hat i+3 hat j-2 hat k and 2 hat i+ hat j+4 hat k are 0,5 and 8 respectively. Find the vector.

Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k and 2 hat i+5 hat j+10 hatk form a tetrahedron in space.

Show that four points whose position vectors are 6 hat i-7 hat j ,\ 16 i-19 hat j-4 hat k ,\ 3 hat i-6 hat k ,\ 2 hat i-5 hat j+10\ hat k are coplanar.

The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,C and D lie on a plane, find the value of lambda .

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