prove that the vectors `|bar b|bar a +|bar a|bar b and |bar b| bar a -| bar a|bar b` are orthogonal to each other

Show that vectors |bar(b)|bar(a)+|bar(a)|bar(b) and |b|bar(a)-|a|bar(b) are orthogonal

Let bar(a) and bar(b) be unit vector.If the vectors bar(c)=bar(a)+2bar(b) and bar(d)=5bar(a)-4bar(b) are perpendicular to the each other then angle between bar(a) and bar(b) is

For unit vectors bar(a) and bar(b) , if bar(a)+2bar(b) and 5bar(a)-4bar(b) are perpendicular to each other then the angle between bar(a) and bar(b) is ………….

Given four non zero vectors bar a,bar b,bar c and bar d . The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

Given four non zero vectors bar a,bar b,bar c and bar d. The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

Given four non zero vectors bar a,bar b,bar c and bar d . The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.

If for unit vectors bar(a) and bar(b),bar(a)+2bar(b) and 5bar(a)-4bar(b) are perpendicular to each other, then (bar(a)^^bar(b))=

bar(a),bar(b),bar(c) are three vectors such that |bar(a)|=1,|bar(b)|=2,|bar(c)|=3 and bar(b),bar(c) are perpendicular to each other.If the projection of bar(b) along bar(a) is same as that of bar(c) along bar(a) then |bar(a)-bar(b)+bar(c)| is equal to

(d) answer ANY one question :1. bar a, bar b and bar c be three vectors such that bar a +bar b+ bar c =0 and |bar a|=1, |bar b|=4,|bar c |=2 . Evlautae bar a.bar b + bar b.bar c+bar c.bar a .