Find `lambda`and `mu` if
`(2overset^^i+6overset^^j+27overset^^k)xx(overset^^i+lambdaoverset^^j+muoverset^^k)=oversetrarr0`.

Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^i+overset^^j+2overset^^k " and " overset^^i+lambdaoverset^^j-3overset^^k are coplanar.

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

Find the angle between the vectors overset^^i-2overset^^j+3overset^^k"and"3overset^^i-2overset^^j+overset^^k.

Show that each of the given three vectors is a unit vector : 1/7(2overset^^i+3overset^^j+6overset^^k),1/7(3overset^^i-6overset^^j+2overset^^k),1/7(6overset^^i+2overset^^j-3overset^^k) . Also, show that the are mutually perpendicular to each other.

Find veca.(vecbxxvecc) ,if veca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k and vecc=3overset^^i+overset^^j+2overset^^k .

Consider the vectors oversetrarra=2overset^^i+3overset^^j+overset^^k " and " oversetrarrb=3overset^^i +2 overset^^j -3overset^^k find oversetrarra.oversetrarrb

Consider oversetrarra=overset^^i+2overset^^j-3overset^^k,oversetrarrb=3overset^^i-overset^^j+2overset^^k "and" oversetrarrc=11 overset^^i+overset^^j : Find the value of lambda "and" mu such that oversetrarrc =lambda oversetrarra+mu oversetrarrb

The position vectors of the points A,B,C are given to be 2overset^^i+overset^^j-overset^^k,overset^^3i-overset^^2j+overset^^k"and" 1overset^^i+4overset^^j-3overset^^k respectively.Prove that A,B,C are collinear

Find the sum of the vectors oversetrarra =overset^^i-2overset^^j+overset^^k,oversetrarrb=-2overset^^i+4overset^^j+5overset^^k " and " oversetrarrc=overset^^i-6overset^^j-7overset^^k

If " " oversetrarra=2overset^^i+2overset^^j+3overset^^k," " oversetrarrb= -overset^^i+2overset^^j+overset^^k " and " oversetrarrc = 3overset^^i+overset^^j are such that oversetrarra+lambda oversetrarrb is perpendicular to oversetrarrc ,then find the value of lambda