Find the value of `lambda` , a non-zero scalar, if `lambda[1 0 2 3 4 5]+2[1 2 3-1-3 2]=[4 4 10 4 2 14]` .

The value of lambda for which the equation lambda^2 - 4lambda + 3+ (lambda^2 + lambda -2)x + 6x^2 - 5x^3 =0 will have two roots equal to zero is

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

The sum of distinct value of lambda for which the system of equations (lambda -1 )x + (3lambda + 1) y + 2 lambda x= 0 (lambda -1) x + (4lambda - 2) y + (lambda + 3) x= 0 2x + (2lambda + 1) y + 3(lambda - 1) z=0 has non - zeor solutions is ______.

Find the value of lambda . If the points A(-1,3,2), B(-4,2,-2) and C(5,lambda,10) are collinear.

The value of lambda for which the points (-2,4,lambda),(3,-6,-8),(1,-2,-2) are collinear is

Find all values of lambda for which the (lambda-1)x+(3 lambda+1)y+2 lambda z=0(lambda-1)x+(4 lambda-2)y+(lambda+3)z=02x+(3 lambda+1)y+3(lambda-1)z possess non-trivial solution and find the ratios x:y:z, where lambda has the smallest of these value.

Find the value of lambda for which the line (x-1)/2=(y-1)/3=(z-1)/lambda is parallel to the plane vecr.(2hati+3hatj+4hatk)=4 .

vec a=2hat i+lambda_(1)hat j+3hat k,vec b=4hat i+(3-lambda_(2))hat j+6hat k and vec c=3hat i+6hat j+(lambda_(3)-1)hat k be three vectors such that vec b=2vec a and vec a is perpendicular to c then a possible value of (lambda_(1),lambda_(2),lambda_(3)) is : (a) (1,3,1)( b) (-(1)/(2),4,0)( c) (1,5,1) (d) ((1)/(2),4,-2)