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Match the statements/expressions given in Column 1 with the values given in Column II. Column I, Column II In `R^2,` iff the magnitude of the projection vector of the vector `alpha hat i+beta hat jon3 hat i+ hat ji s3` and if `alpha=2+3beta` , then possible value (s) of `|alpha|` is (are), p. 1 Let `aa n db` be real numbers such that the function `f(x)={-3a x^2-2, x<1b x+a^2, xgeq1` is Differentiable for all `x in Rdot` Then possible value (s) of a is(are), q. 2 Let `omega!=1` be a complex cube root of unit. If `(3-3omega+2omega^2)^(4n)+(2+3omega-3omega^2)^(4n+3)+(-3+2omega+3omega^2)^(4n+3)=0` , then possible value (s) of `n` is (are), r. 3 Let the harmonic mean of two positive real numbers `aa n db` be 4. If `q` is a positive real number such tht `a ,5,q ,b` is an arithmetic progression, then the value (s) of `|q-a|` is (are), s. 4 , t 5

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Match the statements/expressions given in column I with the values given in Column II. Column I, Column II In R^2, if the magnitude of the projection vector of the vector alpha hat i+beta hat j on sqrt(3) hat i+ hat ji ssqrt(3) and if |alpha| is /are, (p) 1 Let aa n db be real numbers such that the function f(x)={-3a x^2-2,x<1b x+a^2, xgeq1 Differentiable for all x in Rdot Then possible value (s) of a is/are, (q) 2 Let omega!=1 be a complex cube root of unity. If (3-3omega+2omega^2)^(4n+3)+(2+3omega-3omega^2)^(4n+3)+(-3-2omega+3omega^2)^(4n+3)=0 , then possible values (s) of n is /are, (r) 3 Let the harmonic mean of two positive real numbers aa n db be 4. If q is a positive real number such that a ,5,q ,b is an arithmetic progressin, then the values (s)of|q-a| is /are, (s) 4 , (t) 5

Write the projection of the vector hat i+3 hat j+7 hat k on the vector 2 hat i-3 hat j+6 hat kdot

Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on the vector vec b=2 hat i+2 hat j+ hat k .

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find the direction cosines of the following vectors: 2 hat i+2 hat j- hat k 6 hat i-2 hat j-3 hat k 3 hat i-4 hat k

Find a vector of magnitude 9, which is perpendicular to both vectors 4 hat i- hat j+3 hat ka n d-2 hat i+ hat j-2 hat k .

The component of the vector barĀ= (2hat i +3 hat j) along the vector barB = (hat i + hat j) is

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

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