Dot product of a vector with hat i+ hat...

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.

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

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, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k vec b = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively form the vertices of a right angled triangle.

Find the projection of the vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat k

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

Show that the four points A, B, C and D with position vectors 4 hat i+5\ hat j+ hat k ,-(\ hat j+ hat k),3 hat j+9\ hat j+4 hat k\ a n d\ 4( hat i+ hat j+ hat k) , respectively are coplanar.

Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

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