If the vectors `alphaoverset^i+3overset^j+overset^k` and `2overset^i+overset^j+overset^k` are perpendicular, what is `alpha`

If the vectors overset^i+2overset^j+overset^k and 2overset^i+3overset^j+alphaoverset^k are perpendicular, then what is alpha ?

If the position vectors of two points A ans B are 3overset^i+2overset^j+overset^k and 2overset^i-5overset^j+4overset^k respectively, what is the magnitude of oversetrarr(AB) ?

Show that the normals to the planes oversettor.(overset^i-overset^j+overset^k)=3 and oversettor.(3overset^i+2overset^j-overset^k)=0 are perpendicular to each other.

If the vectors _a^rarr=2overset^j-3overset^k and _b^rarr=2overset^j+aoverset^j+6overset^k are parallel, white the value of alpha .

Write the values of m and n for which the vectors (m-1)overset^i+(n+2)overset^j+4overset^k and (m+1)overset^i+(n-2)overset^j+8overset^k are parallel

Show that the vectors overset^i+overset^j-2overset^k,overset^i-2overset^j+overset^k and 2overset^i-overset^j-overset^k are the sides of an equilateral triangle.

Show that the vectors 3overset^i-4overset^j-4overset^k,2overset^i-overset^j+overset^k and overset^i-3overset^j-5overset^k from a right angled tringle.

Find the vector of magniltude 5 units and parallel to the resultant of the vectors oversetrarra=2overset^i+3overset^j-overset^k and oversetrarrb=overset^i-2overset^j+overset^k then find the angle between oversetrarra+oversetrarrb and oversetrarra-oversetrarrb .

What is the value of x of the vectors 3overset^i-7overset^j-4overset^k,3overset^i-2overset^j+overset^k and overset^i+overset^j+xoverset^k

Find the equation of the plane passing through the intersection of the planes _r^"-"=(overset^i+overset^j+overset^k)=1 and _r^"-"=(overset^2i+overset^3j+overset^k)+4=0 and parallel to x=axis.