### QNO.1) Prove that i*(a*i)+j*(a*j)+k*(a*k)=2a where i,j,k are mutually perpendicular unit vectors along coordinate axes. QNO.2) If a,b,c be 3 unit vectors such that a*(b*c)=b/2. Find the angles which a makes with b and c, where b and c are being non parallel vectors. QNO.3)Show that the vectors a*(b*c), b*(c*a) and c*(a*b) are coplanar.

October 21, 2019

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### QNo.1) Find the value of p such that the vector 2i-j+l, i+1j+2k and 3i+pj+5k are coplanar. QNo.2) if the vectors ai+j+k, i+bj+k and i+j+ck are coplanar then show that; then show that-: 1/(1-a)+1/(1-n)+1/(1-c)=1 QNo.3) If a,b,c be the 3 non-cp;mar vectors such that a=a1l+a2m+a3 b=b1l+b2m+b3n  and  c=c1l+c2m+c3n then show that [a b c]= determinant [l m n]

October 21, 2019

QNo.2) if the vectors ai+j+k, i+bj+k and i+j+ck are coplanar then show that; then show that-: 1/(1-a)+1/(1-n)+1/(1-c)=1     QNo.3) If a,b,c be […]