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Let L be the line of intersection of pla...

Let L be the line of intersection of planes `vec(r).(hat(i) - hat(j) + 2hat(k)) = 2` and `vec(r).(2hat(i) + hat(j) - hat(k)) = 2`. If `P(alpha, beta, gamma)` is the foot of perpendicular on L from the point (1,2,0), then the value of `35(alpha + beta + gamma)` is equal to :

A

101

B

119

C

143

D

134

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Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) and vec(b) then x equals

Knowledge Check

  • The position of a particle is given by vec(r )= (hat(i) + 2hat(j) - hat(k)) and momentum vec(P)= (3 hat(i) + 4 hat(j)-2 hat(k)) . The angular momentum is perpendicular to

    A
    X-axis
    B
    Y-axis
    C
    Z-axis
    D
    Line at equal angles to all the three axes

  • If angle bisector of vec(a) = 2hat(i) + 3hat(j) + 4hat(k) and vec(b) = 4hat(i) - 2hat(j) + 3 hat(k) is vec(c) = alpha hat(i) + 2hat(j) + beta hat(k) then :

    A
    `vec(c). hat(k) + 7= 0`
    B
    `vec(c) .hat(k) - 14 = 0`
    C
    `vec(c) .hat(k) + 14 = 0 `
    D
    `vec(c) .hat(k) - 7 =0`

  • Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) and vec(b) then x equals

    A
    0
    B
    1
    C
    `-4`
    D
    `-2`
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