The scalar product of the vector `hati+3hatj+3hatk` with a unit vector along the sum of vectors `hati-3hatj+4hatk` and `lambdahati-4hatj+5hatk`is equal to one. Find the value of `lambda`.

The scalar product of the vector hati+2hatj+2hatk with a unit vector along the sum of vectors 3hati-4hatj+6hatk and lambdahati-3hatj+4hatk is equal to one. Find the value of lambda .

The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of vectors 2hati+4hatj-5hatk and lambdahati+2hatj+3hatk is equal to one. Find the value of lambda .

The scalar product of the vector veca=hati+hatj+hatk with a unit vector along the sum of vectors vecb=2hati+4hatj-5hatk and vecc=lambdahati+2hatj+3hatk is equal to one. Find the value of 'lambda' and hence find the unit vector along vecb+vecc .

Find a unit vector parallel to the sum of the vectors hati+hatj+hatk and 2hati-3hatj+5hatk .

The unit vector perpendicular to the vectors 6hati+2hatj+3hatk and 3hati-6hatj-2hatk , is

Find the unit vector parallel to the resultant vector of 2hati+4hatj-5hatk and hati+2hatj+3hatk .

Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3hatk