If `overline A = i+j+k and overlineB=2i+j` find (a) `A.B` (b) `AtimesB`​

Let overline a be vectors parallel to line of intersection of planes p_1 and p_2 through origin. If p_1 is parallel to the vectors 2overline j + 3 overline k and 4overline j - 3 overline k and p_2 is parallel to overline j - overline k and 3overline i - 3overline j, then the angle between overline a and 2overline i + overline j - 2overlinek is (A) pi/2 (B) pi/4 (C) pi/3 (D) pi/6

If overline(a)=hat(i)+hat(j)+hat(k), overline(b)=2hat(i)+qhat(j)+hat(k), overline(c)=hat(i)-hat(j)+4hat(k) and overline(a)*(overline(b)timesoverline(c))=1 , then q=

If overline(a)=hat(i)+hat(j)+hat(k), overline(b)=2hat(i)+lambdahat(j)+hat(k), overline(c)=hat(i)-hat(j)+4hat(k) and overline(a)*(overline(b)timesoverline(c))=10 , then lambda is equal to

If a=3i+2j+k, b=5i-j+2k" and "c=i+j+k , find [a b c]

If overline(a)=hat(i)+2hat(k), overline(b)=2hat(i)+hat(j), overline(c)=hat(j)+2hat(k) , then overline(a)*(overline(b)timesoverline(c))=

If overline(a)=3hat(i)-2hat(j)+7hat(k), overline(b)=5hat(i)+hat(j)-2hat(k), overline(c)=hat(i)+hat(j)-hat(k) , then overline(a)*(overline(b)timesoverline(c))=

The value of k for which the vectors overline(a)=hat(i)-hat(j) and overline(b)=-2hat(i)+khat(j) are colllinear is

If vectors overline(a)=2hat(i)+3hat(j)+4hat(k), overline(b)=hat(i)+hat(j)+5hat(k) and overline(c) form a left handed system, then overline(c) is

If overline(a)=7hat(i)-hat(j)+2hat(k), overline(b)=hat(i)+3hat(j)-hat(k), overline(c)=4hat(i)+5hat(k) , then overline(a)*(overline(b)timesoverline(c))=