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Find the sum of vectos a = hat(i)- 2hat(...

Find the sum of vectos `a = hat(i)- 2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k)` and `c=hat(i)-6hat(j)-7hat(k)`.

Text Solution

Verified by Experts

Here , given `a=hat(i)-2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k),c=hat(i)-6hat(j)-7hat(k)` Sum of these vectors can be calculated by adding their `hat(i),hat(j) and hat(k)` components.
`therefore vec(a)+vec(b)+vec(c ) = (hat(i) -2hat(j)+hat(k))+(-2hat(i)+4hat(j)+5hat(k))+(hat(i)-6hat(j)-7hat(k))`
`= (hat(i)-2hat(i)+hat(i))+(-2hat(j)+4hat(j)-6hat(j))+(hat(k)+5hat(k)-7hat(k))`.
`=0hat(i) -4hat(j)-hat(k)=-4hat(j)-hat(k)`.
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Show that the points A, B and C with position vectors , vec(a)=3hat(i)-4hat(j)-4hat(k),vec(b)=2hat(i) -hat(j)+hat(k) and vec (c ) hat(i) -3hat(j)-5hat(k) respectively, from the vertices of a right angled triangle.

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Knowledge Check

  • The value of p such that the vectors hat(i) + 3hat(j) - 2hat(k), 2hat(i) - hat(j) + 4hat(k) and 3hat(i) + 2hat(j) + p hat(k) are coplanar is

    A
    4
    B
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    C
    8
    D
    10

  • Three forces (2 hat(i) - 3hat(j) + 4hat(k)),(8hat(i) - 7hat(j) + 6hat(k)) and m(hat(i) - hat(j) + hat(k) keep a body in equilibirium. The value of m is:

    A
    10
    B
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    C
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    D
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  • Let vec(a) =hat(i) +2hat(j) +hat(k),vec(b) =hat(i) -hat(j) +hat(k) and vec(c ) =hat(i) +hat(j) -hat(k) , vector in the plane of vec(a) and vec(b) whose projection on vec(c ) is 1/(sqrt(3)) is ______.

    A
    `4hat(i) +hat(j) -4hat(k)`
    B
    `4hat(i) - hat(j) +4hat(k)`
    C
    `3hat(i)+hat(j)-3hat(k)`
    D
    `hat(i) +hatj -2hat(k)`

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