Question

if 2i-j-3k, 3i+2j+k, i+mj+4k are coplanar , find the value of m​

Answer 1

Answer:

Three vectors, a, b, c are coplanar if [abc]=0

or

∣

∣

∣

∣

∣

∣

∣

∣

2

1

3

−1

2

λ

1

−3

5

∣

∣

∣

∣

∣

∣

∣

∣

=0

or 2(10+3λ)+1(5+9)+1(λ−6)=0 ( expanding along first row.)

or 7λ+28=0∴λ=−4

Step-by-step explanation:

hope it is helpfull

Answer 2

The value of m is -4.

Given,

Three coplanar vectors 2i-j-3k, 3i+2j+k,and i+mj+4k.

To Find,

The value of m.

Solution,

For three vectors to be coplanar [abc} = 0

Now, [abc} is the determinant of the given three vectors.

$\left[\begin{array}{ccc}2&-1&1\\1&2&-3\\3&m&5\end{array}\right]$

Now, on expanding the expanding along the first row, we get

2(10+3m)+1(5+9)+1(m−6)=0

20+6m+14+m-6 = 0

28+6m = 0

m = -28/6

m = -4

Hence, the value of m is -4.

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