The vector which can give unit vector along `x` -axis with `A=2hat i-4hat j+7k,B=7hat i+2hat j-5k` and `C=-4hat i+7hat j+3hat k` is

The scalar product of the vector hat i+hat j+hat k with the unit vector along the sum of vectors 2hat i+4hat j-5hat k. and lambdahat i+2hat j+3hat k is equal to one.Find the value of lambda .

The magnitude of the vector product of the vector hat i+hat j+hat k with a unit vector along the sum of vectors 2hat i+4hat j-5hat k and lambda i+2hat j+3hat k is equal to sqrt(2). Find the value of lambda_(.)

Find the sum of vectors vec a=hat i-2hat j+hat k,vec b=-2hat i+4hat j+5hat k and vec c=hat i-6hat j-7hat k

Find the sum of the vectors vec a=hat i-2hat j+hat k,vec b=-2hat i+4hat j+5hat k and vec c=hat i-6hat j-7hat k

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k

Prove that the four points having position vectors are non-coplanar; 3hat i+hat j-hat k,2hat i-hat j+7hat k and 7hat i-hat j+23hat k

Write a unit vector in the direction of the sum of the vectors vec a=2hat i+2hat j-5hat k and vec b=2hat i+hat j-7hat k

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

Prove that the following vectors are non- coplanar: 3hat i+hat j-hat k,2hat i-hat j+7hat k and 7hat i-hat j+23hat khat i+2hat j+3hat k,2hat i+hat j+3 and hat i+hat j+hat k

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear