[" If the vectors "bar(a)=i+j+k],[bar(b)=i-j+k,bar(c)=2i+3j+mk" are "],[" coplanar,then "m=..]

Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+betabar(b) . If the vectors bar(i)-2bar(j)+bar(k), 3bar(i)+2bar(j)-bar(k) and bar(c) are coplanar then alpha/beta equals

If vectors i + j + k,i - j+k and 2i + 3j + mk are coplanar, then m =

If the vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) + 2bar(j)-3bar(k), bar(c ) = 3bar(i) + pbar(j) +5bar(k) are coplanar then find p.

Find the unit vector in the direction of the sum of the vectors bar(a) = 2bar(i)+ 2bar(j) - 5bar(k) and bar(b) = 2bar(i) + bar(j) + 3bar(k) .

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

If bar(i)-2bar(j), 3bar(j)+bar(k), lambdabar(i)+3bar(j) are coplanar then lambda=

If the vectors bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), and bar(c)=bar(i)+alphabar(j)+betabar(k) are linearly dependent and abs(bar(c))=sqrt(3) then show that alpha=pm1, beta=1

Prove that vectors bar(a) = 2bar(i) -bar(j) + bar(k), bar(b) = bar(i) -bar(3j)-5bar(k) and bar(c ) = 3bar(i) - 4bar(j) -4bar(k) are coplanar.

If there vectors bar(a)=bar(i)+bar(j)+bar(k) , bar(b)=bar(i)-2a^(2)bar(j)+abar(k) , bar(c)=bar(i)+(a+1)bar(j)-abar(k) are linearly dependent vectors then the real a lies in the interval.

Find the value of lambda such that the vectors bar(a)=2bar(i)+lambda bar(j)+bar(k) and bar(b)=bar(i)+2bar(j)+3bar(k) are orthogonal …….