[" If "a,b" and "c" are non-coplanar vectors and if "d" is such that "],[d=(1)/(x)(a+b+c)" and "a=(1)/(y)(b+c+d)]

If bar(a), bar(b)&bar(c) are non-coplanar vectors and if bar(d) is such that bar(d)=1/x(bar(a)+bar(b)+bar(c)) and bar(d)=1/y(bar(b)+bar(c)+bar(d)) where x and y are non-zero real numbers, then 1/(xy)(bar(a)+bar(b)+bar(c)+bar(d))=

If a, b and c are non-coplanar vectors and d=lambda vec a+mu vec b+nu vec c , then lambda is equal to

a , b , c are three non coplanar non zero vectors and r is any vector in space, then ( a × b )×( r × c )+( b × c )×( r × a )+( c × a )×( r × b ) is equal to) [ ⃗ [2a b ⃗ c ] ⃗ r b. 2 [ ⃗ a ⃗ b ⃗ c ] ⃗ r c. 3 [ ⃗ a ⃗ b ⃗ c ] ⃗ r d. none of these

Property 5: Vectors a; b and c are non- coplanar iff vectors a'; b' and c' are non- coplanar.

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,